Squares

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ACT Math › Squares

Questions 1 - 10

Find the area of a square with side length 5.

Explanation

To solve, simply use the formula for the area of a square given side length s. Thus,

The perimeter of a square is 48. What is the length of its diagonal?

$12\sqrt{2}$

$\sqrt{12}$

$24\sqrt{2}$

$48\sqrt{2}$

$2\sqrt{12}$

Explanation

Perimeter = side * 4

48 = side * 4

Side = 12

We can break up the square into two equal right triangles. The diagonal of the sqaure is then the hypotenuse of these two triangles.

Therefore, we can use the Pythagorean Theorem to solve for the diagonal:

$\sqrt{144+144}=\sqrt{hypotenuse^2}$

$hypotenuse=\sqrt{2\times 144}=\sqrt{2\times 12\times 12}=12\sqrt{2}$

The perimeter of a square is 48. What is the length of its diagonal?

$12\sqrt{2}$

$\sqrt{12}$

$24\sqrt{2}$

$48\sqrt{2}$

$2\sqrt{12}$

Explanation

Perimeter = side * 4

48 = side * 4

Side = 12

We can break up the square into two equal right triangles. The diagonal of the sqaure is then the hypotenuse of these two triangles.

Therefore, we can use the Pythagorean Theorem to solve for the diagonal:

$\sqrt{144+144}=\sqrt{hypotenuse^2}$

$hypotenuse=\sqrt{2\times 144}=\sqrt{2\times 12\times 12}=12\sqrt{2}$

Find the area of a square with side length 5.

Explanation

To solve, simply use the formula for the area of a square given side length s. Thus,

The area of a square is $64\textup{ in}^2$ , what is the perimeter of the square?

$\textup{32in}$

$\textup{16in}$

$\textup{36in}$

$\textup{Not enough information is provided.}$

Explanation

Since the sides of a square are all the same, the area of a square can be found by $\textup{side}*\textup{side}=64\textup{in}^2.$ Therefore, the side of the square must be $8\textup{in}.$ The perimeter of a square can be found by adding up all of the four sides: $\textup{8in+8in+8in+8in=32in.}$

The area of a square is $64\textup{ in}^2$ , what is the perimeter of the square?

$\textup{32in}$

$\textup{16in}$

$\textup{36in}$

$\textup{Not enough information is provided.}$

Explanation

The area of a square is $25 cm^{2}$ . If the square is enlarged by a factor of 2, what is the perimeter of the new square?

$40\ cm$

$50\ cm$

$75\ cm$

$80\ cm$

$100\ cm$

Explanation

The area of a square is given by $A = s^{2}$ so we know the side is 5 cm. Enlarging by a factor of two makes the new side 10 cm. The perimeter is given by , so the perimeter of the new square is 40 cm.

How much more area does a square with a side of 2r have than a circle with a radius r? Approximate π by using 22/7.

12/14 square units

1/7 square units

4/7 square units

6/7 square units

Explanation

The area of a circle is given by A = πr2 or 22/7r2

The area of a square is given by A = s2 or (2r)2 = 4r2

Then subtract the area of the circle from the area of the square and get 6/7 square units.

The area of a square is $25 cm^{2}$ . If the square is enlarged by a factor of 2, what is the perimeter of the new square?

$40\ cm$

$50\ cm$

$75\ cm$

$80\ cm$

$100\ cm$

Explanation

How much more area does a square with a side of 2r have than a circle with a radius r? Approximate π by using 22/7.

12/14 square units

1/7 square units

4/7 square units

6/7 square units

Explanation

The area of a circle is given by A = πr2 or 22/7r2

The area of a square is given by A = s2 or (2r)2 = 4r2

Then subtract the area of the circle from the area of the square and get 6/7 square units.

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