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ACT Math : Quadrilaterals

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #161 : Quadrilaterals

Find the area of a square whose side length is .

Possible Answers:

Correct answer:

Explanation:

To find area, simply square the side length. Thus,

A=1^2=1

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Example Question #391 : Geometry

Find the area of a square with side length 5.

Possible Answers:

Correct answer:

Explanation:

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

A=s^2=5^2=25

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Example Question #843 : Basic Geometry

Square

A square is circumscribed on a circle with a 6 inch radius. What is the area of the square, in square inches?

Possible Answers:

144

$36\pi$

Correct answer:

144

Explanation:

We know that the radius of the circle is also half the length of the side of the square; therefore, we also know that the length of each side of the square is 12 inches.

Square

We need to square this number to find the area of the square.

A=s^2

A=12^2

A=144

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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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ACT Math : Quadrilaterals

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #161 : Quadrilaterals

Example Question #391 : Geometry

Example Question #843 : Basic 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 #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

All ACT Math Resources

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