ISEE Middle Level Math : Geometry

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

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Example Questions

Example Question #5 : How To Find The Perimeter Of Square

A new building in New York City will have a footprint that is a perfect square, taking up a complete city block. If one city block is \(\displaystyle 1/8\)of a mile, what is the perimeter of the building?

Possible Answers:

\(\displaystyle 1mi\)

\(\displaystyle \frac{2}{3}mi\)

\(\displaystyle \frac{1}{2}mi\)

\(\displaystyle \frac{1}{4}mi\)

Correct answer:

\(\displaystyle \frac{1}{2}mi\)

Explanation:

A new building in New York City will have a footprint that is a perfect square, taking up a complete city block. If one city block is \(\displaystyle 1/8\)of a mile, what is the perimeter of the building?

 

To find the perimeter of a square, we need to multiply the side length by 4.

Our side length is \(\displaystyle 1/8\) mile, so do the following to find our answer:

\(\displaystyle 4*\frac{1}{8}=\frac{4}{8}=\frac{1}{2}mi\)

So the perimeter is \(\displaystyle \frac{1}{2}mi\)

Example Question #1 : Quadrilaterals

Use the following to answer the question.

Square1

Find the perimeter of the square.

Possible Answers:

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

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

\(\displaystyle 24\text{ft}\)

\(\displaystyle 36\text{ft}\)

\(\displaystyle 12\text{ft}\)

Correct answer:

\(\displaystyle 24\text{ft}\)

Explanation:

To find the perimeter of a square, we use the following formula:

\(\displaystyle \text{perimeter of square} = a+b+c+d\)

where a, b, c, and d are the lengths of each side. 

 

Now, we know that a square has equal sides.  So given the square

Square1

we know that each side equals 6ft.  So, we can use this to substitute into the formula.  We get

\(\displaystyle \text{perimeter of square} = 6\text{ft} + 6\text{ft} + 6\text{ft} + 6\text{ft}\)

\(\displaystyle \text{perimeter of square} = 24\text{ft}\)

Example Question #4 : How To Find The Perimeter Of Square

Find the perimeter of a square with a width of 8 inches.

Possible Answers:

\(\displaystyle 64 \text{ inches}\)

\(\displaystyle 32 \text{ inches}^2\)

\(\displaystyle 64 \text{ inches}^2\)

\(\displaystyle 32\text{ inches}\)

\(\displaystyle \text{There is not enough information to answer the question.}\)

Correct answer:

\(\displaystyle 32\text{ inches}\)

Explanation:

To find the perimeter of a square, we use the following formula:

\(\displaystyle \text{perimeter of square} = a+b+c+d\)

where a, b, c, and d are the lengths of the sides of the square.  

 

Now, we know the width of the square is 8 inches.  Because it is a square, we know all sides are equal.  Therefore, all sides are 8 inches.  Knowing this, we can substitute into the formula.  We get

\(\displaystyle \text{perimeter of square} = 8\text{ inches} +8\text{ inches} +8\text{ inches} +8\text{ inches}\)

\(\displaystyle \text{perimeter of square} = 32 \text{ inches}\)

Example Question #2 : Quadrilaterals

You are playing Monopoly and notice that the dice is a cube. If the dice has a height of 2 centimeters, what is the perimeter of one of its surfaces?

Possible Answers:

\(\displaystyle 4cm\)

\(\displaystyle 16cm\)

Cannot be determined from the information provided.

\(\displaystyle 8 cm\)

Correct answer:

\(\displaystyle 8 cm\)

Explanation:

You are playing Monopoly and notice that the dice is a cube. If the dice has a height of 2 centimeters, what is the perimeter of one of its surfaces?

Begin by realizing that we need to find the perimeter of a square.

Next, recall that the height of a cube is the same as its length and width. In other words, one surface of a cube will be a square with sides equal to the height of the cube.

Armed with this knowledge, we can find the perimeter of the square.

\(\displaystyle P=4s\)

\(\displaystyle P=4*2cm=8cm\)

So our answer is 8cm

Example Question #2 : Squares

A square stamp has an edge length of 6 centimeters, what is its perimeter?

Possible Answers:

\(\displaystyle 24 cm\)

\(\displaystyle 36cm\)

\(\displaystyle 12cm\)

\(\displaystyle 18cm\)

Correct answer:

\(\displaystyle 24 cm\)

Explanation:

A square stamp has an edge length of 6 centimeters, what is its perimeter?

To find the perimeter of a square, we simply can multiply the edge length by 4.

Doing so yields:

\(\displaystyle P_{square}=6cm*4=24cm\)

Example Question #3 : How To Find The Perimeter Of Square

Find the perimeter of a square that has a base of length 9 inches.

Possible Answers:

\(\displaystyle 81\text{in}\)

\(\displaystyle 54\text{in}\)

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

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

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

Correct answer:

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

Explanation:

To find the perimeter of a square, we will use the following formula:

\(\displaystyle \text{perimeter of square} = a+b+c+d\)

where a, b, c, and d are the lengths of each side of the square.

 

Now, we know the base has a length of 9 inches.  Because it is a square, we know that all sides are equal.  Therefore, all sides are 9 inches.  Knowing this, we can substitute into the formula.  We get

\(\displaystyle \text{perimeter of square} = 9\text{in} +9\text{in} +9\text{in} +9\text{in}\)

\(\displaystyle \text{perimeter of square} = 36\text{in}\)

Example Question #11 : How To Find The Perimeter Of Square

A city block is a perfect square with sides of \(\displaystyle \frac{1}{2}mile\).

What is the perimeter of the city block?

Possible Answers:

\(\displaystyle 1\frac{1}{2}mi^2\)

\(\displaystyle 2mi\)

\(\displaystyle 1mi\)

\(\displaystyle 1mi^2\)

Correct answer:

\(\displaystyle 2mi\)

Explanation:

A city block is a perfect square with sides of \(\displaystyle \frac{1}{2}mile\).

What is the perimeter of the city block?

To find the perimeter of a square, simply multiply the side length by 4:

\(\displaystyle A=4*\frac{1}{2}mi=\frac{4}{2}mi=2mi\)

So our answer is 2 miles

Example Question #12 : Quadrilaterals

Find the perimeter of a square with a length of 7in.

Possible Answers:

\(\displaystyle 21\text{in}\)

\(\displaystyle 14\text{in}\)

\(\displaystyle 28\text{in}\)

\(\displaystyle 49\text{in}\)

\(\displaystyle 32\text{in}\)

Correct answer:

\(\displaystyle 28\text{in}\)

Explanation:

To find the perimeter of a square, we will use the following formula:

\(\displaystyle \text{perimeter of square} =a+b+c+d\)

where a, b, c, and d are the lengths of the sides of the square.

 

Now, we know the length of the square is 7in.  Because it is a square, we know all sides are equal.  Therefore, all sides are 7in.

Knowing all of this, we can substitute into the formula.  We get

\(\displaystyle \text{perimeter of square} = 7\text{in} +7\text{in} +7\text{in} +7\text{in}\)

\(\displaystyle \text{perimeter of square} = 28\text{in}\)

Example Question #13 : How To Find The Perimeter Of Square

Use the following image to answer the question:

Square3

Find the perimeter of the square.

Possible Answers:

\(\displaystyle \text{There is not enough information to solve the problem.}\)

\(\displaystyle 64\text{cm}\)

\(\displaystyle 16\text{cm}\)

\(\displaystyle 24\text{cm}\)

\(\displaystyle 32\text{cm}\)

Correct answer:

\(\displaystyle 32\text{cm}\)

Explanation:

To find the perimeter of a square, we will use the following formula:

\(\displaystyle \text{perimeter of square} = a+b+c+d\)

where a, b, c, and d are the lengths of the sides of the square.

 

Now, let's look at the given square.

Square3

We can see that one side is 8cm.  Because it is a square, all sides are equal.  Therefore, all sides are 8cm.  

Knowing this, we can substitute into the formula.  We get

\(\displaystyle \text{perimeter of square} = 8\text{cm} + 8\text{cm} + 8\text{cm} + 8\text{cm}\)

\(\displaystyle \text{perimeter of square} = 32\text{cm}\)

Example Question #14 : How To Find The Perimeter Of Square

Find the perimeter of a square with a length of 9cm.

Possible Answers:

\(\displaystyle \text{There is not enough information to solve the problem.}\)

\(\displaystyle 18\text{cm}\)

\(\displaystyle 27\text{cm}\)

\(\displaystyle 81\text{cm}\)

\(\displaystyle 36\text{cm}\)

Correct answer:

\(\displaystyle 36\text{cm}\)

Explanation:

To find the perimeter of a square, we will use the following formula:

\(\displaystyle \text{perimeter of square} = a+b+c+d\)

where a, b, c, and d are the lengths of the sides of the square.

 

Now, we know the length of the square is 9cm.  Because it is a square, all of the sides are equal.  Therefore, all sides are 9cm.

Knowing this, we can substitute into the formula.  We get

\(\displaystyle \text{perimeter of square} = 9\text{cm} + 9\text{cm} + 9\text{cm} + 9\text{cm}\)

\(\displaystyle \text{perimeter of square} = 36\text{cm}\)

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