Pentagons

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ACT Math › Pentagons

Questions 1 - 10

A regular pentagon has a side length of . Find its perimeter.

Explanation

Because we're told the pentagon is a regular polygon, this means that all of its sides are the same length. That is, the side lengths are congruent.

In order to solve for the perimeter, which is the sum of all sides, we can use a multiplication shortcut of:

$P=l \cdot n$ , where is perimeter, is length of the sides, and is the number of sides of the polygon.

Using the information given in the problem, the values can be substituted in.

Note that this math is the same as adding five times:

One side of a regular pentagon is . Find the perimeter of the pentagon.

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 .

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

A regular pentagon has a side length of . Find its perimeter.

Explanation

Because we're told the pentagon is a regular polygon, this means that all of its sides are the same length. That is, the side lengths are congruent.

In order to solve for the perimeter, which is the sum of all sides, we can use a multiplication shortcut of:

$P=l \cdot n$ , where is perimeter, is length of the sides, and is the number of sides of the polygon.

Using the information given in the problem, the values can be substituted in.

Note that this math is the same as adding five times:

One side of a regular pentagon is . Find the perimeter of the pentagon.

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 .

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

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

Explanation

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

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

Explanation

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

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

Explanation

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

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

Explanation

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

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

$6+6\sqrt{5}$

$5 + 5\sqrt{6}$

Explanation

Use the formula for the diagonal of a pentagon:

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

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

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

$6+6\sqrt{5}$

$5 + 5\sqrt{6}$

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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