ISEE Middle Level Math : Quadrilaterals

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

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Example Questions

Example Question #11 : How To Find The Area Of A Square

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

Possible Answers:

\displaystyle 12cm^2

\displaystyle 54cm^2

\displaystyle 36cm^2

\displaystyle 24cm^2

Correct answer:

\displaystyle 36cm^2

Explanation:

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

To find the area of a square, simply square the side length:

\displaystyle A_{square}=s^2=(6cm)^2=36cm^2

So our answer is 

\displaystyle 36cm^2

Example Question #12 : How To Find The Area Of A Square

If you have a square deck, what is the area when one of the sides is \displaystyle 10 feet?

Possible Answers:

\displaystyle 50ft^2

\displaystyle 20ft^2

\displaystyle 40ft^2

\displaystyle 100ft^2

Correct answer:

\displaystyle 100ft^2

Explanation:

The area of a square is the side length square, or multiplied by itself,

\displaystyle A=s^2

meaning your answer must be,

\displaystyle s=10

\displaystyle A=10^{2}=100ft^2.

Example Question #11 : How To Find The Area Of A Square

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

What is the area of the city block?

Possible Answers:

\displaystyle 1mi^2

\displaystyle \frac{1}{8}mi^2

\displaystyle \frac{1}{4}mi^2

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

Correct answer:

\displaystyle \frac{1}{4}mi^2

Explanation:

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

What is the area of the city block?

To find the area of a square, take the side length and square it.

\displaystyle A_{square}=s^2=(\frac{1}{2}mi)^2=\frac{1}{2}mi*\frac{1}{2}mi=\frac{1}{4}mi^2

So, we get:

\displaystyle \frac{1}{4}mi^2

Example Question #43 : Quadrilaterals

Find the area of a square with a base of length 13 inches.

Possible Answers:

\displaystyle 26\text{in}

\displaystyle 52\text{in}^2

\displaystyle 169\text{in}^2

\displaystyle 169\text{in}

\displaystyle 52\text{in}

Correct answer:

\displaystyle 169\text{in}^2

Explanation:

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

\displaystyle \text{area of square} = l \cdot w

where l is the length and w is the width of the square.

 

Now, we know the base of the square has a length of 13 inches.  Because it is a square, we know that all sides are equal.  Therefore, the width is also 13 inches.  Knowing this, we can substitute into the formula.  We get

\displaystyle \text{area of square} = 13\text{in} \cdot 13\text{in}

\displaystyle \text{area of square} = 169\text{in}^2

Example Question #1963 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Find the area of a square with a base of length 8 inches.

Possible Answers:

\displaystyle 32\text{in}^2

\displaystyle 16\text{in}^2

\displaystyle 64\text{in}^2

\displaystyle 32\text{in}

\displaystyle 64\text{in}

Correct answer:

\displaystyle 64\text{in}^2

Explanation:

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

\displaystyle \text{area of square} = l \cdot w

where l is the length and w is the width of the square.

 

Now, we know the base has a length of 8 inches.  Because it is a square, we know that all sides are equal.  Therefore, all sides have a length of 8 inches.  This means the width is also 8 inches.  Knowing this, we can substitute into the formula.  We get

\displaystyle \text{area of square} = 8\text{in} \cdot 8\text{in}

\displaystyle \text{area of square} = 64\text{in}^2

Example Question #41 : Quadrilaterals

Find the area of a square with a base of 12 inches.

Possible Answers:

\displaystyle 144\text{in}^2

\displaystyle 48\text{in}^2

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

\displaystyle 144\text{in}

\displaystyle 48\text{in}

Correct answer:

\displaystyle 144\text{in}^2

Explanation:

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

\displaystyle \text{area of square} = l \cdot w

where l is the length and w is the width of the square.

 

Now, we know the base of the square is 12in.  Because it is a square, we know that all sides are equal.  Which means all sides are 12in.  Therefore, the width is also 12in.  Knowing this, we can substitute into the formula.  We get

\displaystyle \text{area of square} = 12\text{in} \cdot 12\text{in}

\displaystyle \text{area of square} = 144\text{in}^2

Example Question #1964 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Find the area of a square with a width of 5 feet.

Possible Answers:

\displaystyle 15\text{ft}^2

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

\displaystyle 10\text{ft}^2

\displaystyle 20\text{ft}^2

\displaystyle 25\text{ft}^2

Correct answer:

\displaystyle 25\text{ft}^2

Explanation:

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

\displaystyle \text{area of square} = l \cdot w

where l is the length and w is the width of the rectangle.

 

Now, we know the width is 5 feet.  Because it is a square, all sides are equal.  This means the length is also 5 feet.

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

\displaystyle \text{area of square} = 5\text{ft} \cdot 5\text{ft}

\displaystyle \text{area of square} = 25\text{ft}^2

Example Question #44 : Squares

Find the area of a square with a width of 12cm.

Possible Answers:

\displaystyle 24\text{cm}^2

\displaystyle 144\text{cm}^2

\displaystyle 48\text{cm}^2

\displaystyle 121\text{cm}^2

\displaystyle 96\text{cm}^2

Correct answer:

\displaystyle 144\text{cm}^2

Explanation:

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

\displaystyle \text{area of square} = l \cdot w

where l is the length and w is the width of the square.

 

Now, we know the width of the square is 12cm.  Because it is a square, all sides are equal.  Therefore, the length is also 12cm.

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

\displaystyle \text{area of square} = 12\text{cm} \cdot 12\text{cm}

\displaystyle \text{area of square} = 144\text{cm}^2

Example Question #48 : Quadrilaterals

Use the following image to answer the question:

Square3

Find the area of the square.

Possible Answers:

\displaystyle 24\text{cm}^2

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

\displaystyle 32\text{cm}^2

\displaystyle 16\text{cm}^2

\displaystyle 64\text{cm}^2

Correct answer:

\displaystyle 64\text{cm}^2

Explanation:

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

\displaystyle \text{area of square} = l \cdot w

where is the length and w is the width of the square.

 

Now, let's look at the given square.

Square3

We can see the width is 8cm.  Because it is a square, we know that all sides are equal.  Therefore, the width is also 8cm.

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

\displaystyle \text{area of square} = 8\text{cm} \cdot 8\text{cm}

\displaystyle \text{area of square} = 64\text{cm}^2

Example Question #41 : Squares

Find the area of a square with a length of 11in.

Possible Answers:

\displaystyle 121\text{in}^2

\displaystyle 100\text{in}^2

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

\displaystyle 22\text{in}^2

\displaystyle 44\text{in}^2

Correct answer:

\displaystyle 121\text{in}^2

Explanation:

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

\displaystyle \text{area of square} = l \cdot w

where l is the length and w is the width of the square.

 

Now, we know the length of the square is 11in.  Because it is a square, all sides are equal.  Therefore, the width is also 11in.

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

\displaystyle \text{area of square} = 11\text{in} \cdot 11\text{in}

\displaystyle \text{area of square} = 121\text{in}^2

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