ISEE Middle Level Quantitative Reasoning - How to find the area of a square

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

$121\text{in}^2$

$100\text{in}^2$

$22\text{in}^2$

$44\text{in}^2$

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

Explanation

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

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

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

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

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

A square has an area of 36, and each side is equal to What is the value of ?

Explanation

Each side of a square is equal to the square root of the area. The square root of 36 is 6, so each side is 6. Thus, 3x (being a side of the square is equal to 6. This means that x is equal to 2 because 3 times 2 is 6.

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

$144\text{cm}^2$

$48\text{cm}^2$

$24\text{cm}^2$

$96\text{cm}^2$

$121\text{cm}^2$

Explanation

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

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

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

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

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

The area of a square is $121\text{in}^2$ . Find the length of one side of the square.

$11\text{in}$

$12\text{in}$

$13\text{in}$

$22\text{in}$

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

Explanation

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

where x is the length of one side.

Now, we want to find the length of one side, so we will solve for x. We know the area of the square is $121\text{in}^2$ . So, we will substitute.

$121\text{in}^2 = x^2$

$\sqrt{121\text{in}^2} = \sqrt{x^2}$

$11\text{in} = x$

$x = 11\text{in}$

Therefore, the length of one side of the square is 11in.

Use the following image to answer the question:

Square3

Find the area of the square.

$64\text{cm}^2$

$32\text{cm}^2$

$16\text{cm}^2$

$24\text{cm}^2$

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

Explanation

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

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

where l 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

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

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

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

What is the area of the city block?

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

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

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

Explanation

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

What is the area of the city block?

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

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

So, we get:

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

Find the area of a square that has a width of 13in.

$169\text{in}^2$

$52\text{in}^2$

$26\text{in}^2$

$118\text{in}^2$

$39\text{in}^2$

Explanation

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

$A = l \cdot w$

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

Now, we know the width of the square is 13in. Because it is a square, all sides are equal. Therefore, the length is also 13in.

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

$A = 13\text{in} \cdot 13\text{in}$

$A = 169\text{in}^2$

Find the area of a square that has a width of 15in.

$225\text{in}^2$

$60\text{in}^2$

$30\text{in}^2$

$125\text{in}^2$

$45\text{in}^2$

Explanation

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

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

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

Now, we know the width of the square is 15in. Because it is a square, all sides are equal. Therefore, the length is also 15in.

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

$\text{area of square} = 15\text{in} \cdot 15\text{in}$

$\text{area of square} = 225\text{in}^2$

Find the area of a square with a base of 9 inches.

$81\text{in}^2$

$81\text{in}$

$36\text{in}^2$

$36\text{in}$

$\text{There is not enough information to answer the question.}$

Explanation

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

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

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

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

$\text{area of square} = 9\text{in} \cdot 9\text{in}$