Elementary School Math Quiz: Solve Perimeter And Area Problems
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Solve Perimeter And Area ProblemsQuestion 1 of 20

Maya has a rectangle that is 10 yards long and 2 yards wide. What is its perimeter?

12 yards
20 yards
24 yards
22 yards
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Elementary School Math Quiz

Elementary School Math Quiz: Solve Perimeter And Area Problems

Practice Solve Perimeter And Area Problems in Elementary School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Solve Perimeter And Area Problems, giving you a quick way to practice the rules, question types, and explanations that matter most for Elementary School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Maya has a rectangle that is 10 yards long and 2 yards wide. What is its perimeter?

  1. 12 yards
  2. 20 yards
  3. 24 yards (correct answer)
  4. 22 yards
Explanation: The perimeter is the sum of all four sides: 10 plus 2 plus 10 plus 2 yards, which is 24 yards, matching choice C. Choice A only adds the length and width once instead of going around all four sides. Choice B comes from multiplying the length and width instead of adding all the sides. Choice D leaves out one of the sides from the total.

Question 2

Look at the grid showing two rectangles. Rectangle P and Rectangle Q have the same area. What is the difference in their perimeters?

  1. 22 units difference in perimeter
  2. 44 units difference in perimeter (correct answer)
  3. 66 units difference in perimeter
  4. 88 units difference in perimeter
Explanation: Rectangle P: 2×6=122 \times 6 = 12 square units, perimeter =2(2)+2(6)=16= 2(2) + 2(6) = 16 units. Rectangle Q: 3×4=123 \times 4 = 12 square units, perimeter =2(3)+2(4)=14= 2(3) + 2(4) = 14 units. Difference =16−14=4= 16 - 14 = 4 units. Choice A is half the correct difference. Choice C results from subtracting lengths (6−3=36 - 3 = 3) plus widths (4−2=24 - 2 = 2). Choice D results from doubling the correct answer.

Question 3

The perimeter of a rectangle is 3434 inches. The longer sides are each 1010 inches. What is the length of each shorter side?

  1. 77 inches (correct answer)
  2. 1414 inches
  3. 1212 inches
  4. 2424 inches
Explanation: Perimeter questions are all about adding up the distances around a shape. A rectangle has two pairs of equal sides — two longer sides and two shorter sides — and the perimeter is the total of all four. When you know the perimeter and one pair of sides, you can work backward to find the other pair. Start by figuring out how much of the perimeter the two longer sides use up. Since each longer side is 1010 inches, together they account for 10+10=2010 + 10 = 20 inches. That leaves 34−20=1434 - 20 = 14 inches for the two shorter sides combined. Because the two shorter sides are equal in length, split that in half: 14÷2=714 \div 2 = 7 inches. So each shorter side is 77 inches, which matches choice A. Choice B (1414 inches) is the total length of both shorter sides combined — a trap if you forget to divide by 2. Choice C (1212 inches) doesn't come from a correct step; it's likely a guess based on numbers close to the given values. Choice D (2424 inches) is what you'd get if you subtracted only one longer side (34−10=2434 - 10 = 24) instead of both, forgetting that a rectangle has two longer sides. A helpful strategy: always remember a rectangle has four sides, not two. When working backward from perimeter, subtract both known sides first, then divide the remainder by 2 to find each unknown side.

Question 4

A square picture frame has a perimeter of 3636 inches. What is the length of one side of the frame?

  1. 66 inches
  2. 88 inches
  3. 99 inches (correct answer)
  4. 1212 inches
Explanation: When a shape is a square, all four sides are the same length. The perimeter is the distance all the way around the shape, which means it's the sum of all four sides. So for any square, you can find one side by dividing the perimeter by 4. Here, the perimeter is 3636 inches, so one side measures 36÷4=936 \div 4 = 9 inches. That matches choice C. You can double-check by adding: 9+9+9+9=369 + 9 + 9 + 9 = 36 inches. ✓ Choice A (66 inches) is the answer you'd get if you divided by 6 instead of 4, which might happen if you confused the number of sides. Choice B (88 inches) doesn't come from any correct step — 8×4=328 \times 4 = 32, not 36, so it can't be right. Choice D (1212 inches) is what you get if you divide by 3 instead of 4, perhaps thinking of a triangle's three sides instead of a square's four sides. A helpful tip: whenever you see "square" in a geometry problem, immediately remember the number 4 — a square has 4 equal sides and 4 equal corners. To find a side from the perimeter, divide by 4. To find the perimeter from a side, multiply by 4. Knowing this simple rule will help you solve many perimeter problems quickly.

Question 5

A regular pentagon (a shape with 55 equal sides) has a perimeter of 4545 cm. What is the length of one side?

  1. 55 cm
  2. 88 cm
  3. 99 cm (correct answer)
  4. 1111 cm
Explanation: When you see a question about the perimeter of a regular shape, remember that "regular" means all sides are equal in length. The perimeter is the total distance around the shape, so it equals the length of one side multiplied by the number of sides. To find one side when you know the perimeter, you reverse that operation by dividing. A pentagon has 55 equal sides, and the perimeter is 4545 cm. So you divide: 45÷5=945 \div 5 = 9 cm. That means each side measures 99 cm, which is choice C. Choice A (55 cm) is a trap — it's the number of sides, not the length of one. Students sometimes confuse the two numbers in the problem. Choice B (88 cm) doesn't come from any correct operation; if each side were 88 cm, the perimeter would be 4040 cm, not 4545. Choice D (1111 cm) is also incorrect — 11×5=5511 \times 5 = 55 cm, which is too big. You can quickly check this by multiplying your answer by 55 to see if you get back to 4545. A helpful strategy: whenever you solve a perimeter problem, plug your answer back in to verify. Here, 9×5=459 \times 5 = 45 ✓. Also, memorize the shape-side pairs you'll see often: triangle (33), square (44), pentagon (55), hexagon (66), octagon (88). Knowing the number of sides instantly is half the battle on these questions.

Question 6

Keisha needs trim around a 10-inch by 2-inch picture frame; what is the perimeter?

  1. 12 inches
  2. 20 inches
  3. 20 square inches
  4. 24 inches (correct answer)
Explanation: This question tests 3rd grade perimeter and area: finding perimeter given sides, finding unknown side lengths, and understanding same perimeter can have different areas or same area can have different perimeters (CCSS.3.MD.8). Perimeter is the distance around a shape, calculated by adding all side lengths, measured in linear units (feet, meters). Area is the space inside a shape, calculated for rectangles by multiplying length × width, measured in square units (square feet, square meters). For rectangles, perimeter = 2×length + 2×width or add all four sides. The picture frame is 10 inches by 2 inches, asking for the perimeter for trim. Choice C is correct because perimeter = 10+2+10+2 = 24 inches or 2×(10+2)=24 inches, showing understanding of perimeter for the border. Choice B represents a common error of multiplying for area (10×2=20) but using linear units, confusing area with perimeter; this happens when students mix operations. To help students: Distinguish perimeter and area with context—fence/border/frame = perimeter (around), carpet/tile/paint = area (inside). Practice both: 'This frame is 10 by 2. Perimeter for trim: 10+2+10+2=24 inches. Area inside: 10×2=20 square inches.' Watch for: Adding only two sides or using multiplication for perimeter.

Question 7

Jayden wants to put a fence around his rectangular yard. The yard is 1515 feet long and 1212 feet wide. Fencing costs $2\$2 per foot. How much will the fencing cost in total?

  1. $27\$27
  2. $54\$54
  3. $108\$108 (correct answer)
  4. $360\$360
Explanation: When a question asks about putting a fence around a shape, it's testing perimeter — the total distance around the outside. Perimeter is different from area (which measures the space inside), so watch for that keyword "around." For a rectangle, perimeter means adding up all four sides. Since a rectangle has two lengths and two widths, you can calculate it as: P=2×length+2×widthP = 2 \times \text{length} + 2 \times \text{width}
P=2×15+2×12=30+24=54 feetP = 2 \times 15 + 2 \times 12 = 30 + 24 = 54 \text{ feet} Jayden needs 5454 feet of fencing. Since each foot costs $2\$2, multiply: 54×2=$10854 \times 2 = \$108 That matches choice C. Choice A ($27\$27) comes from only adding one length and one width (15+12=2715 + 12 = 27) — that's just half the perimeter. Choice B ($54\$54) is the perimeter in feet, but forgets to multiply by the $2\$2 per foot cost. Choice D ($360\$360) uses area instead of perimeter (15×12=18015 \times 12 = 180, then ×2=360\times 2 = 360) — a common trap when you confuse "around" with "inside." Study tip: Circle the key word in word problems. "Around," "border," "fence," and "frame" all signal perimeter (add all sides). "Cover," "inside," "carpet," and "paint" signal area (multiply length × width). Getting this first step right is half the battle!

Question 8

A hexagon has six sides. Five of the sides measure 44 cm, 66 cm, 33 cm, 55 cm, and 77 cm. If the perimeter is 2828 cm, what is the length of the sixth side?

  1. 22 cm
  2. 33 cm (correct answer)
  3. 44 cm
  4. 55 cm
Explanation: When a shape's perimeter is given, remember that it's just the total distance around the shape — the sum of all its side lengths. If you know the perimeter and all but one side, you can find the missing side by subtracting the known sides from the total. Start by adding the five known sides:
4+6+3+5+7=25 cm4 + 6 + 3 + 5 + 7 = 25 \text{ cm} Since the full perimeter is 2828 cm, the sixth side must make up the difference:
28−25=3 cm28 - 25 = 3 \text{ cm} That matches choice B. Choice A (22 cm) is what you'd get if you added the known sides incorrectly and got 2626 instead of 2525 — a common slip when adding several numbers in a row. Choice C (44 cm) is a trap because 44 cm is already listed as one of the given sides; the question isn't asking you to repeat a value. Choice D (55 cm) is another number pulled straight from the given sides, which tempts students who guess instead of calculating. A helpful strategy: whenever a perimeter problem gives you all but one side, write it as a subtraction sentence — Perimeter - (sum of known sides) = missing side. Double-check your addition by grouping numbers that make friendly tens (like 3+7=103 + 7 = 10 and 4+6=104 + 6 = 10, then add 55) to avoid arithmetic mistakes.

Question 9

A rectangle has an area of 3636 square inches. Which set of side lengths would give this rectangle the SMALLEST perimeter?

  1. 11 in by 3636 in
  2. 22 in by 1818 in
  3. 44 in by 99 in
  4. 66 in by 66 in (correct answer)
Explanation: When a question asks about area and perimeter together, remember that they measure different things. Area is the space inside (length × width), while perimeter is the distance around (2×length+2×width2 \times \text{length} + 2 \times \text{width}). A helpful pattern to know: when the area stays the same, the rectangle whose sides are closest to equal (most "square-like") will always have the smallest perimeter. Long, skinny rectangles have huge perimeters even when their area matches. Check each choice by calculating the perimeter:
  • A) 1×361 \times 36: perimeter =2(1)+2(36)=74= 2(1) + 2(36) = 74 inches
  • B) 2×182 \times 18: perimeter =2(2)+2(18)=40= 2(2) + 2(18) = 40 inches
  • C) 4×94 \times 9: perimeter =2(4)+2(9)=26= 2(4) + 2(9) = 26 inches
  • D) 6×66 \times 6: perimeter =2(6)+2(6)=24= 2(6) + 2(6) = 24 inches
All four rectangles have an area of 3636 square inches, but D has the smallest perimeter because its sides are equal — it's a square. A is wrong because a 1×361 \times 36 rectangle is extremely long and thin, giving the largest perimeter. B is wrong for the same reason — still very stretched out. C is closer to square-shaped and has a smaller perimeter than A or B, but it's still not as compact as D. Tip: For a fixed area, the closer a rectangle's sides are to equal, the smaller the perimeter. A square is always the winner!

Question 10

Lena has 3232 feet of ribbon to make a rectangular border. She wants the border to be as close to a square as possible using whole-number side lengths. What should the side lengths be?

  1. 11 ft by 1515 ft
  2. 44 ft by 1212 ft
  3. 77 ft by 99 ft
  4. 88 ft by 88 ft (correct answer)
Explanation: This question is about perimeter — the distance around a shape. For a rectangle, perimeter = 2×(length+width)2 \times (\text{length} + \text{width}). When you're told the ribbon is 32 feet, that's your total perimeter, so length + width must equal 32÷2=1632 \div 2 = 16 feet. Now you just need two whole numbers that add to 16 and are as close to equal as possible (that's what "as close to a square" means). Checking option D: 8+8=168 + 8 = 16, and 2×16=322 \times 16 = 32 feet of ribbon. The two sides are exactly equal, making it a perfect square — which is as "close to square" as you can get. Option A (1+15=161 + 15 = 16) uses the right amount of ribbon but the sides are very far apart, making a long skinny rectangle — the opposite of square. Option B (4+12=164 + 12 = 16) also uses 32 feet of ribbon but the sides differ by 8, so it's not close to square. Option C (7+9=167 + 9 = 16) works for the perimeter and is close to square (sides differ by 2), but D is even closer since the sides are identical. Tip: When a perimeter problem asks for the "most square" rectangle, first divide the perimeter by 2 to find length + width, then look for the pair of whole numbers closest to each other. Equal sides always win when they're an option.

Question 11

The perimeter of a rectangle is 2424 cm. If the width is 44 cm, what is the area of the rectangle?

  1. 2020 square cm
  2. 3232 square cm (correct answer)
  3. 4848 square cm
  4. 8080 square cm
Explanation: When you see a rectangle problem that gives you perimeter and one side, the trick is to work backwards to find the missing side before you can calculate area. Remember two key formulas: perimeter = 2×(length+width)2 \times (\text{length} + \text{width}) and area = length×width\text{length} \times \text{width}. Start with the perimeter. Since 2×(length+width)=242 \times (\text{length} + \text{width}) = 24, you know that length+width=12\text{length} + \text{width} = 12 cm. The width is 4 cm, so the length must be 12−4=812 - 4 = 8 cm. Now find the area: 8×4=328 \times 4 = 32 square cm, which matches choice B. Choice A (20) comes from mistakenly subtracting the width from half the perimeter and then something similar — a common slip when students confuse perimeter and area steps. Choice C (48) is a trap: it's what you'd get if you thought the length was 12 (forgetting to subtract the width) and multiplied 12×412 \times 4. Choice D (80) comes from multiplying the full perimeter's half incorrectly or multiplying 20×420 \times 4, mixing up the operations entirely. A good strategy for these two-step problems: always write down which formula you need first. Circle what the question gives you (perimeter, width) and what it asks for (area). Find the missing side before jumping to the final calculation. Rushing to multiply the numbers you see is the most common trap on rectangle problems.

Question 12

A rectangle has area 24 square feet, and its length is 6 feet. What is its width?

  1. 30 feet
  2. 4 feet (correct answer)
  3. 18 feet
  4. 12 feet
Explanation: Area equals length times width, so 24 divided by 6 gives a width of 4 feet. Choice A comes from adding instead of dividing. Choice C comes from subtracting the length from the area instead of dividing. Choice D comes from dividing incorrectly and mismatching units.

Question 13

A rectangle has a perimeter of 24 meters. One side is 7 meters. What is the combined length of the other two sides?

  1. 10 meters (correct answer)
  2. 3 meters
  3. 7 meters
  4. 5 meters
Explanation: Since opposite sides of a rectangle are equal, the two sides of length 7 meters total 14 meters, leaving 24 minus 14, which is 10 meters, for the other two sides combined. Choice B (3 meters) comes from a subtraction error. Choice C (7 meters) repeats the given side length instead of finding the remaining total. Choice D (5 meters) is the length of just one of the two remaining sides, not their combined length.

Question 14

Sofia is buying carpet for a rectangular room that is 9 feet long and 4 feet wide. What is the area of the room?

  1. 36 square feet (correct answer)
  2. 13 square feet
  3. 26 square feet
  4. 18 square feet
Explanation: The area of the room is 9 times 4, which is 36 square feet. Choice B (13 square feet) comes from adding 9 and 4 instead of multiplying. Choice C (26 square feet) uses the perimeter formula instead of the area formula. Choice D (18 square feet) comes from doubling only one side instead of multiplying both.

Question 15

Refer to the figure. What is the perimeter of the shape?

  1. 2121 cm
  2. 2626 cm
  3. 2828 cm
  4. 3030 cm (correct answer)
Explanation: Adding all six sides going around the figure: 7+5+3+3+4+8=307 + 5 + 3 + 3 + 4 + 8 = 30 cm. Choice A adds only some of the sides. Choice B misses one side. Choice C double-counts or misreads a segment.

Question 16

Refer to the table showing four rectangles. Which two rectangles have the SAME area but DIFFERENT perimeters?

  1. Rectangle 1 and Rectangle 2
  2. Rectangle 1 and Rectangle 3 (correct answer)
  3. Rectangle 2 and Rectangle 4
  4. Rectangle 3 and Rectangle 4
Explanation: Areas: R1: 2×12=242 \times 12 = 24; R2: 3×6=183 \times 6 = 18; R3: 4×6=244 \times 6 = 24; R4: 5×5=255 \times 5 = 25. Perimeters: R1: 2828; R2: 1818; R3: 2020; R4: 2020. Rectangles 1 and 3 both have area 2424 but perimeters 2828 and 2020 (different). Choice A: different areas. Choice C: different areas. Choice D: same perimeter but different areas — this is the opposite of what is asked.

Question 17

Two rectangles both have a perimeter of 2020 cm. Rectangle X measures 22 cm by 88 cm. Rectangle Y measures 55 cm by 55 cm. How much larger is the area of Rectangle Y than Rectangle X?

  1. 00 square cm (they are equal)
  2. 33 square cm
  3. 99 square cm (correct answer)
  4. 2525 square cm
Explanation: This question tests an important idea in geometry: two shapes can have the same perimeter but different areas. Perimeter measures the distance around a shape, while area measures the space inside it. For rectangles, area = length × width. Start by finding each area. Rectangle X is 2×8=162 \times 8 = 16 square cm. Rectangle Y is 5×5=255 \times 5 = 25 square cm. To find how much larger Y is, subtract: 25−16=925 - 16 = 9 square cm. That matches choice C. Choice A is a trap for students who assume that equal perimeters mean equal areas — but as this problem shows, a square-like shape holds more area than a long, thin rectangle with the same perimeter. Choice B (33) likely comes from subtracting the side lengths (8−5=38 - 5 = 3) instead of the areas — that's comparing dimensions, not space inside. Choice D (2525) is just the area of Rectangle Y by itself; it forgets to subtract Rectangle X's area to find the difference. A helpful pattern to remember: among rectangles with the same perimeter, the closer the shape is to a square, the larger its area. A 5×55 \times 5 square beats a skinny 2×82 \times 8 rectangle every time. When a word problem asks "how much larger," always finish by subtracting — don't stop after calculating just one value.

Question 18

Carlos is fencing a square playground. He has 48 feet of fencing, and he uses all of it to build the square fence. Later, he wants to add a path across the middle of the playground, parallel to one side. How much additional fencing does he need for this path?

  1. 6 feet of additional fencing
  2. 12 feet of additional fencing (correct answer)
  3. 24 feet of additional fencing
  4. 48 feet of additional fencing
Explanation: Since the playground is a square made from 48 feet of fencing, each side is 48 divided by 4, or 12 feet. A path across the middle, parallel to one side, is the same length as one side, so Carlos needs 12 feet of additional fencing, matching choice B. Choice A is too short to reach across the playground. Choices C and D use the wrong amount of fencing, mixing up parts of the original square with the new path.

Question 19

Garden B is a rectangle that is 5 feet by 5 feet. What is its area?

  1. 9 square feet
  2. 20 square feet
  3. 25 square feet (correct answer)
  4. 10 square feet
Explanation: Area equals length times width, so 5 times 5 equals 25 square feet. Choice A is the area of a different garden shape, not this one. Choice B is the perimeter of the garden, not its area. Choice D comes from adding the side lengths instead of multiplying them.

Question 20

A rectangle has a perimeter of 26 yards, and one side is 8 yards long. What is the length of the other side?

  1. 5 yards (correct answer)
  2. 18 yards
  3. 9 yards
  4. 13 yards
Explanation: The perimeter equals twice the sum of both side lengths, so 2 x 8 plus 2 times the other side equals 26, which gives the other side as (26 minus 16) divided by 2, or 5 yards, making Choice A correct. Choice B (18 yards) comes from subtracting 8 from 26 without accounting for both pairs of sides. Choice C (9 yards) does not match any consistent method for solving this problem. Choice D (13 yards) divides the perimeter by 2 but forgets to subtract the known side first.