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ACT Math : Plane Geometry

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Example Questions

Example Question #21 : Act Math

Find the length of one side for a regular pentagon with a perimeter of 115 .

Possible Answers:

Correct answer:

Explanation:

Use the formula for perimeter to solve for the side length:

P=5s

115=5s

s=23

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

Find the length of each side for a regular pentagon with a perimeter of 14{,}000 .

Possible Answers:

2{,}480

2{,}800

2{,}900

2{,}600

Correct answer:

2{,}800

Explanation:

Use the formula for perimeter to solve for the side length:

P=5s

14,000=5s

s=2,800

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Example Question #1 : How To Find The Length Of The Diagonal Of A Pentagon

If the side of a pentagon is , what is the diagonal of the pentagon?

Possible Answers:

$\frac{1+\sqrt5}{4}$

$1+\sqrt5$

$\frac{1+\sqrt5}{2}$

$\frac{1+\sqrt5}{8}$

$\frac{2+\sqrt10}{2}$

Correct answer:

$1+\sqrt5$

Explanation:

Write the formula for finding the diagonal of a pentagon.

$d=\frac{1+\sqrt5}{2}s$

Plug in the side length and simplify.

$d=\frac{1+\sqrt5}{2}(2)= 1+\sqrt5$

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Example Question #1 : How To Find The Length Of The Diagonal Of A Pentagon

Find the length of the diagonal for a pentagon with a a side length of .

Possible Answers:

$5 + 5\sqrt{6}$

$6+6\sqrt{5}$

Correct answer:

$6+6\sqrt{5}$

Explanation:

Use the formula for the diagonal of a pentagon:

$d=\frac{s(1+\sqrt{5})}{2}$

$d=\frac{12(1+\sqrt{5})}{2}=6+6\sqrt{5}$

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Example Question #21 : Plane Geometry

Find the length of the diagonal for a pentagon with a perimeter of .

Possible Answers:

$3+3\sqrt{5}$

$4+4\sqrt{5}$

$6+6\sqrt{5}$

$2+2\sqrt{5}$

Correct answer:

$3+3\sqrt{5}$

Explanation:

1. Use the formula for perimeter to solve for the side length:

P=5s

30=5s

s=6

2. Use the formula for the diagonal of a pentagon:

$d=\frac{s(1+\sqrt{5})}{2}$

$d=\frac{6(1+\sqrt{5})}{2}=3+3\sqrt{5}$

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Example Question #21 : Geometry

Find the diagonal for a pentagon with a perimeter of .

Possible Answers:

$\frac{5(1+\sqrt{5})}{2}$

$\frac{7(1+\sqrt{6})}{2}$

$\frac{4(1+\sqrt{3})}{2}$

$\frac{3(6+\sqrt{5})}{2}$

Correct answer:

$\frac{5(1+\sqrt{5})}{2}$

Explanation:

1. Use the formula for perimeter to solve for the side length:

P=5s

25=5s

s=5

2. Use the formula for the diagonal of a pentagon:

$d=\frac{s(1+\sqrt{5})}{2}$

$d=\frac{5(1+\sqrt{5})}{2}$

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Example Question #2 : How To Find The Length Of The Diagonal Of A Pentagon

If a side of the pentagon is , what is the diagonal of the pentagon?

Possible Answers:

$1+\sqrt5$

$12\sqrt5$

$6+6\sqrt5$

$12+12\sqrt5$

Correct answer:

$6+6\sqrt5$

Explanation:

Write the diagonal formula for a pentagon.

$d=\frac{1+\sqrt5}{2}s$

Substitute the side length and find the diagonal.

$d=\frac{1+\sqrt5}{2}(12) = (1+\sqrt5)(6) = 6+6\sqrt5$

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Example Question #21 : Plane Geometry

Suppose the side length of a pentagon is . What is the area of the pentagon?

Possible Answers:

$2\sqrt{10+10\sqrt5}$

$4\sqrt{25+10\sqrt5}$

$4\sqrt{5+5\sqrt5}$

$2\sqrt{5+5\sqrt5}$

$\sqrt{25+10\sqrt5}$

Correct answer:

$4\sqrt{25+10\sqrt5}$

Explanation:

Write the formula for the area of a pentagon.

$A=\frac{1}{4}s^2\sqrt{5(5+2\sqrt5)}$

Substitute the side length and simplify the radical.

$A=\frac{1}{4}(4)^2\sqrt{5(5+2\sqrt5)}$

$A=4\sqrt{5(5+2\sqrt5)}$

$A=4\sqrt{25+10\sqrt5}$

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Example Question #23 : Geometry

One side of a regular pentagon is {}12cm . Find the perimeter of the pentagon.

Possible Answers:

80cm

144cm

52cm

60cm

70cm

Correct answer:

60cm

Explanation:

In a regular pentagon, all of the sides are the same length.

The perimeter can then be found by summing all sides or multiplying by .

$12+12+12+12+12=12\times5=60cm$

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Example Question #2 : How To Find The Perimeter Of A Pentagon

Pent2751

What is the perimeter of the regular pentagon pictured above?

Possible Answers:

7.5625

The answer cannot be determined.

6.875

15.75

13.75

Correct answer:

13.75

Explanation:

The key word in this question is "regular." Since the pentagon is regular, all of its sides are equal. This means that it, in fact, looks like:

Pent2752

The perimeter for this is simply 5*2.75 or 13.75 .

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ACT Math : Plane Geometry

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #21 : Act Math

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

Example Question #1 : How To Find The Length Of The Diagonal Of A Pentagon

Example Question #1 : How To Find The Length Of The Diagonal Of A Pentagon

Example Question #21 : Plane Geometry

Example Question #21 : Geometry

Example Question #2 : How To Find The Length Of The Diagonal Of A Pentagon

Example Question #21 : Plane Geometry

Example Question #23 : Geometry

Example Question #2 : How To Find The Perimeter Of A Pentagon

All ACT Math Resources

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