ISEE Lower Level Math : ISEE Lower Level (grades 5-6) Mathematics Achievement

Study concepts, example questions & explanations for ISEE Lower Level Math

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Example Questions

Example Question #2 : How To Find The Area Of A Square

The perimeter of a square is \(\displaystyle 48\; in\).  What is the area?

Possible Answers:

\(\displaystyle 144\; in^{2}\)

\(\displaystyle 100\; in^{2}\)

\(\displaystyle 121\; in^{2}\)

\(\displaystyle 169\; in^{2}\)

\(\displaystyle 81\; in^{2}\)

Correct answer:

\(\displaystyle 144\; in^{2}\)

Explanation:

The perimeter of a square is given by \(\displaystyle P=4s\),  or \(\displaystyle 4s=48\). Divide by four to get \(\displaystyle s=12\).

The area of a square is given by \(\displaystyle A=s^{2}\). Substitute the value obtained from the perimeter equation to get \(\displaystyle A=s^{2}=(12)^{2}=144 \; in^{2}\).

 

Example Question #3 : How To Find The Area Of A Square

The perimeter of a square is \(\displaystyle 20\; in\) .  What is the area?

Possible Answers:

\(\displaystyle 24\; in^{2}\)

\(\displaystyle 9\; in^{2}\)

\(\displaystyle 12\; in^{2}\)

\(\displaystyle 25\; in^{2}\)

\(\displaystyle 16\; in^{2}\)

Correct answer:

\(\displaystyle 25\; in^{2}\)

Explanation:

The perimeter of a square is given by \(\displaystyle P=4s\),  or \(\displaystyle 4s=20\). Divide by four to get \(\displaystyle s=5\).

The area of a square is given by \(\displaystyle A=s^{2}\). Substitute the side length obtained from the perimeter equation to get \(\displaystyle A=s^{2}=(5)^{2}=25 \; in^{2}\).

Example Question #1 : How To Find The Area Of A Square

What is the area of a square with a side that measures \(\displaystyle 5\) feet?

Possible Answers:

\(\displaystyle 25\) square feet

\(\displaystyle 20\) square feet

\(\displaystyle 10\) square feet

\(\displaystyle 15\) square feet

Correct answer:

\(\displaystyle 25\) square feet

Explanation:

The area of a square can be found using the following formula:

\(\displaystyle A=s^{^{2}}\)

The side measures \(\displaystyle 5\) feet. 

\(\displaystyle 5^{2}=25\)

Therefore, the area of the square is \(\displaystyle 25\) square feet.

Example Question #1 : How To Find The Area Of A Square

Becca takes a square napkin and folds it in half once. She then folds it in half again. When she unfolds it, the creases create lines. What best describes the pattern created by the creases?

Possible Answers:

2 squares

2 rectangles

4 rectangles

4 squares

Correct answer:

4 squares

Explanation:

When a napkin is folded in half once, a crease is created vertically down the middle of the napkin. When folded in half once again, another crease is created horizontally across the middle. This creates four squares. Therefore, the best answer is "4 squares."

Example Question #1 : How To Find The Area Of A Square

A square has a perimeter of 24 inches. What is the area of the square?

Possible Answers:

\(\displaystyle 72\text{in}^2\)

\(\displaystyle 24\text{in}^2\)

\(\displaystyle 12\text{in}^2\)

\(\displaystyle 36\text{in}^2\)

\(\displaystyle 6\text{in}^2\)

Correct answer:

\(\displaystyle 36\text{in}^2\)

Explanation:

Given that all four sides of a square are equal, if the perimeter is 24 inches, then you need to divide by 4 to find the length of each side.

\(\displaystyle P=s+s+s+s=4s\)

\(\displaystyle P=24\)

\(\displaystyle P\div4=s\)

\(\displaystyle 24\text{in}\div4=6\text{in}\)

The area is found by multiplying two sides together.

\(\displaystyle A=s\times s\)

Plug in the value of \(\displaystyle s\) to solve.

\(\displaystyle 6\text{in}\times 6\text{in} = 36\text{in}^2\)

Therefore, \(\displaystyle 36\text{in}^2\) is the correct answer. 

Example Question #82 : Squares

The perimeter of a square is 44 inches. What is the area?

Possible Answers:

\(\displaystyle 132\ \text{in}^2\)

\(\displaystyle 111\ \text{in}^2\)

\(\displaystyle 88\ \text{in}^2\)

\(\displaystyle 101\ \text{in}^2\)

\(\displaystyle 121\ \text{in}^2\)

Correct answer:

\(\displaystyle 121\ \text{in}^2\)

Explanation:

In a square, all four sides are equal, and the area is calculated by multiplying one side by itself.

\(\displaystyle A=s\times s=s^2\)

To find the length of one side, we divide the perimeter by 4 (since there are 4 sides of the square).

\(\displaystyle P=s+s+s+s=4s\)

\(\displaystyle s=P\div4\)

We know the perimeter, allowing us to solve for the side.

\(\displaystyle s=44\div4\)

\(\displaystyle s=11\)

This gives us 11, so we know that each side is 11 inches long. Now we can find the area.

\(\displaystyle A=s\times s=11\times 11=121\)

The area, 11 inches times 11 inches, is 121 square inches, the correct answer. 

 

Example Question #232 : Geometry

A square has an area of 49 square inches. What is the length of one side of the square?

Possible Answers:

\(\displaystyle 3.5\ \text{in}\)

\(\displaystyle 7\ \text{in}\)

\(\displaystyle 4\ \text{in}\)

\(\displaystyle 9\ \text{in}\)

\(\displaystyle 8\ \text{in}\)

Correct answer:

\(\displaystyle 7\ \text{in}\)

Explanation:

In a square, all four sides are equal, and the area is calculated by multiplying one side by itself. 

\(\displaystyle A=s\times s=s^2\)

Given that the area is 49 square inches, the length of one side of square would be 7, because 7 times 7 is 49. 

\(\displaystyle 49=s\times s\)

\(\displaystyle 49=7\times7\)

\(\displaystyle s=7\)

Example Question #81 : Squares

If the perimeter of a square is 48 inches, how many square inches are in the area?

Possible Answers:

\(\displaystyle 98\)

\(\displaystyle 36\)

\(\displaystyle 144\)

\(\displaystyle 112\)

Correct answer:

\(\displaystyle 144\)

Explanation:

The perimeter of a square is equal to the sum of the 4 sides. Given that all the sides of a square are equal, the length of one side of the square can be found by dividing the perimeter by 4. 

Given that 48 divided by 4 is equal to 12, we can now find the area. The area is equal to one side multiplied by another. The result is \(\displaystyle 12\cdot12=144\)

Example Question #84 : Squares

If the perimeter of a square is 48 inches, what is the area?

Possible Answers:

\(\displaystyle 100 \; in^{2}\)

\(\displaystyle 144 \; in^{2}\)

\(\displaystyle 169 \; in^{2}\)

\(\displaystyle 121 \; in^{2}\)

\(\displaystyle 81 \; in^{2}\)

Correct answer:

\(\displaystyle 144 \; in^{2}\)

Explanation:

The perimeter of a square is given by \(\displaystyle P=4s\), where \(\displaystyle s\) is the sidelength.  

Plug in the given value for the perimeter:

\(\displaystyle P=4s=48\) 

Divide both sides by 4 to find the sidelength:

\(\displaystyle s=12\; in\)

The area of a square is given by \(\displaystyle A=s^{2}\)

Plug in the sidelength we just calculated to find the area:

\(\displaystyle A=s^{2}=(12)^{2}=144\; in^{2}\)

Example Question #85 : Squares

If the perimeter of a square is 40 centimeters, what is the area?

Possible Answers:

\(\displaystyle 125\; cm^{2}\)

\(\displaystyle 100\; cm^{2}\)

\(\displaystyle 160\; cm^{2}\)

\(\displaystyle 150\; cm^{2}\)

\(\displaystyle 80\; cm^{2}\)

Correct answer:

\(\displaystyle 100\; cm^{2}\)

Explanation:

The perimeter of a square is given by \(\displaystyle P=4s\), where \(\displaystyle s\) is the sidelength. 

We know the perimeter, so we can set up an equation to find the sidelength:

\(\displaystyle P=4s=40\) 

Divide both sides by 4 to isolate the sidelength:

\(\displaystyle s=10\; cm\)

The area of a square is given by \(\displaystyle A=s^{2}\).

We just calculated the sidelength, so now we can find the area:

\(\displaystyle A=s^{2}=(10)^{2}=100\; cm^{2}\)

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