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ISEE Upper Level Math : How to find the area of a square

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Example Questions

Example Question #11 : Squares

One of your holiday gifts is wrapped in a cube-shaped box.

If one of the edges has a length of 6 inches, what is the area of one side of the box?

Possible Answers:

18in^2

36 in^2

36 in

12in^2

Correct answer:

36 in^2

Explanation:

One of your holiday gifts is wrapped in a cube-shaped box.

If one of the edges has a length of 6 inches, what is the area of one side of the box?

We are asked to find the area of one side of a cube, in other words, the area of a square.

We can find the area of a square by squaring the length of the side.

$A_{square}=s^2=(6in)^2=36in^2$

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Example Question #21 : Squares

Inscribed circle

In the above diagram, the circle is inscribed inside the square. The circle has area 30. What is the area of the square?

Possible Answers:

$60 \pi$

$120 \pi$

$\frac{60}{\pi}$

$\frac{120}{\pi}$

Correct answer:

$\frac{120}{\pi}$

Explanation:

Inscribed circle

In terms of , the area of the circle is equal to

$A_{1} = \pi r^{2}$ .

Each side of the square has length equal to the diameter, 2 r , so its area is the square of this, or

$A_{2} = (2r)^{2} = 4 r^{2}$

Therefore, the ratio of the area of the square to that of the circle is

$\frac{A_{2} }{A_{1} } = \frac{4 r^{2}}{\pi r^{2}}= \frac{4}{\pi }$

Therefore, the area of the circle is multiplied by this ratio to get the area of the square:

$A_{1} \cdot \frac{A_{2} }{A_{1} } =A_{1} \cdot \frac{4}{\pi }$

$A_{2} =A_{1} \cdot \frac{4}{\pi }$

Substituting:

$A_{2} = 30 \cdot \frac{4}{\pi } = \frac{120}{\pi }$

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Example Question #22 : Squares

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

Possible Answers:

$18\text{cm}^2$

$81\text{cm}^2$

$36\text{cm}^2$

$54\text{cm}^2$

$72\text{cm}^2$

Correct answer:

$81\text{cm}^2$

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 base (or length) of the square is 9cm. Because it is a square, all sides are equal. Therefore, the width is also 9cm.

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

$\text{area of square} = 9\text{cm} \cdot 9\text{ccm}$

$\text{area of square} = 81\text{cm}^2$

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

While out walking, you find a strange, square-shaped piece of metal. If the side length of the piece is 26 inches, what is the area of the square?

Possible Answers:

54in^2

104in^2

676in^2

786in^2

Correct answer:

676in^2

Explanation:

While out walking, you find a strange, square-shaped piece of metal. If the side length of the piece is 26 inches, what is the area of the square?

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

A=s^2=(26in)^2=676in^2

So, our answer is:

676in^2

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Example Question #24 : Squares

What is the area of the square with a side length of $2\sqrt{3}$ ?

Possible Answers:

Correct answer:

Explanation:

Write the formula for the area of a square.

A=s^2

Substitute the side into the formula.

$A=(2\sqrt{3})^2$

$A = 4\cdot 3 = 12$

The answer is:

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All ISEE Upper Level Math Resources

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ISEE Upper Level Math : How to find the area of a square

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

All ISEE Upper Level Math Resources

Example Questions

Example Question #11 : Squares

Example Question #21 : Squares

Example Question #22 : Squares

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

Example Question #24 : Squares

All ISEE Upper Level Math Resources

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