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ACT Math : Plane Geometry

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Example Questions

Example Question #1 : How To Find The Perimeter Of A Square

A square garden has an area of 64 square feet. If you add 3 feet to each side, what is the new perimeter of the garden?

Possible Answers:

121

Correct answer:

Explanation:

By finding the square root of the area of the garden, you find the length of one side, which is 8. We add 3 feet to this, giving us 11, then multiply this by 4 to get 44 feet for the perimeter.

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Example Question #1 : How To Find The Perimeter Of A Square

The area of the shaded region of a square is 18. What is the perimeter of the square?

Possible Answers:

Correct answer:

Explanation:

The area of the shaded region, which covers half of the square is 18 meaning that the total area of the square is 18 x 2, or 36. The area of a square is equal to the length of one side squared. Since the square root of 36 is 6, the length of 1 side is 6. The perimeter is the length of 1 side times 4 or 6 x 4.

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Example Question #851 : Basic Geometry

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?

Possible Answers:

$40\ cm$

$100\ cm$

$80\ cm$

$75\ cm$

$50\ cm$

Correct answer:

$40\ cm$

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 P = 4s , so the perimeter of the new square is 40 cm.

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Example Question #161 : Quadrilaterals

The diagonal of a square has a length of 10 inches. What is the perimeter of the square in inches squared?

Possible Answers:

$20\sqrt{2}$

$6\sqrt{2}$

$10\sqrt{2}$

$5\sqrt{2}$

Correct answer:

$20\sqrt{2}$

Explanation:

Using the Pythagorean Theorem, we can find the edge of a side to be √50, by 2a²=10². This can be reduced to 5√2. This can then be multiplied by 4 to find the perimeter.

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Example Question #401 : Geometry

What is the perimeter of a square with an area of ?

Possible Answers:

Correct answer:

Explanation:

1. Find the side lengths:

$Area= (side)^{2}$

$36=(side)^{2}$

side=6

2. Use the side lengths to find the perimeter:

Perimeter= 4(side)

Perimeter=4(6)=24

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Example Question #1 : How To Find The Perimeter Of A Square

Find the perimeter of a square whose area is .

Possible Answers:

Correct answer:

Explanation:

To solve, you must first find the side length.

$s=\sqrt{A}=\sqrt{16}=4$

Then, you must multiply the side length by 4 since there are 4 sides. Thus,

P=4*4=16

In this case, volume and perimeter were the same numerical value, but this won't always be the case.

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Example Question #1 : How To Find The Perimeter Of A Square

Find the perimeter of a square with side length .

Possible Answers:

Correct answer:

Explanation:

To find perimeter, simply multiply side length by . Thus,

$P=1\cdot 4=4$

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Example Question #171 : Quadrilaterals

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

Possible Answers:

$\textup{36in}$

$\textup{32in}$

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

$\textup{16in}$

24in

Correct answer:

$\textup{32in}$

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: $\textup{8in+8in+8in+8in=32in.}$

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Example Question #3 : How To Find The Length Of The Side Of A Square

If the area of the square is 100 square units, what is, in units, the length of one side of the square?

Possible Answers:

Correct answer:

Explanation:

$Area = Length \times Length$

100 = (Length)^2

$Length = \sqrt{100}=10$

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Example Question #1 : How To Find The Length Of The Side Of A Square

In Square SQUA , $SU = \sqrt{2x}$ . Evaluate in terms of .

Possible Answers:

$\sqrt{x}$

$x\sqrt{2}$

$2\sqrt{x}$

Correct answer:

$\sqrt{x}$

Explanation:

If diagonal $\overline{SU}$ of Square SQUA is constructed, then $\bigtriangleup SQU$ is a 45-45-90 triangle with hypotenuse $SU = \sqrt{2x}$ . By the 45-45-90 Theorem, the sidelength can be calculated as follows:

$SQ = \frac{SU}{\sqrt{2}} = \frac{\sqrt{2x}}{\sqrt{2}} = \sqrt{\frac{2x}{2}} = \sqrt{x}$ .

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ACT Math : Plane Geometry

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : How To Find The Perimeter Of A Square

Example Question #1 : How To Find The Perimeter Of A Square

Example Question #851 : Basic Geometry

Example Question #161 : Quadrilaterals

Example Question #401 : Geometry

Example Question #1 : How To Find The Perimeter Of A Square

Example Question #1 : How To Find The Perimeter Of A Square

Example Question #171 : Quadrilaterals

Example Question #3 : How To Find The Length Of The Side Of A Square

Example Question #1 : How To Find The Length Of The Side Of A Square

All ACT Math Resources

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