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High School Math : Pentagons

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Example Question #1 : Pentagons

What is the interior angle measure of any regular pentagon?

Possible Answers:

108

Correct answer:

108

Explanation:

To find the angle of any regular polygon you find the number of sides . For a pentagon, n=5 .

You then subtract 2 from the number of sides yielding 3.

Take 3 and multiply it by 180 degrees to yield the total number of degrees in the regular pentagon. 3*180=540

Then to find one individual angle we divide 540 by the total number of angles 5, $\frac{540}{5}=108$

The answer is 108 .

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Example Question #1 : How To Find An Angle In A Pentagon

What is the measure of each interior angle of a regular pentagon?

Possible Answers:

108^o

180^o

120^o

90^o

Correct answer:

108^o

Explanation:

The following equation can be used to determine the measure of an interior angle of a regular polygon, where $\small n$ equals the number of sides.

$\angle=\frac{180(n-2)}{n}$

In a pentagon, $\small n=5$ .

$\angle=\frac{180(5-2)}{5}$

Now we can solve for the angle.

$\angle=\frac{180(3)}{5}=\frac{540}{5}=108^o$

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Example Question #1 : How To Find An Angle In A Pentagon

Find the interior angle of the following regular pentagon:

Angle_length_of_side_pentagon

Possible Answers:

$114^{\circ}$

$108^{\circ}$

$110^{\circ}$

$112^{\circ}$

$116^{\circ}$

Correct answer:

$108^{\circ}$

Explanation:

The formula for the sum of the interior angles of a polygon is

$X=(s-2)(180^{\circ})$ ,

where is the number of sides in the polygon

Plugging in our values, we get:

$X=(5-2)(180^{\circ})$

$X=540^{\circ}$

Dividing the sum of the interior angles by the number of angles in the polygon, we get the value for each interior angle:

$\frac{X}{5}=\frac{540^{\circ}}{5}=108^{\circ}$

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Example Question #1 : How To Find An Angle In A Pentagon

What is the measure of an interior angle of a regular pentagon?

Possible Answers:

108

120

Correct answer:

108

Explanation:

The measure of an interior angle of a regular polygon can be determined using the following equation, where equals the number of sides:

$\angle=\frac{180(n-2)}{n}$

$\angle=\frac{180(5-2)}{5}=\frac{180(3)}{5}=108$

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Example Question #1 : Pentagons

What is the perimeter of the pentagon?

Question_9

Possible Answers:

Correct answer:

Explanation:

The perimeter of a polygon is found by calculating the sum of all of the side lengths. In this instance, the polygon is regular, so the perimeter can be found by mulitplying the length of one side by the total number of sides:

$P=l\times n=6\times 5=30$

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Example Question #6 : Pentagons

Find the length of the diagonal of the following pentagon:

Area_pentagon

Possible Answers:

$3.4\ m$

$3.2\ m$

$3.0\ m$

$3.3\ m$

$3.1\ m$

Correct answer:

$3.4\ m$

Explanation:

Use the Pythagorean Theorem to find the length of the diagonal:

$(\frac{1}{2}side)^2+(apothem)^2=(diagonal)^2$

A^2+B^2 = C^2

$(2\ m)^2+(2.75\ m)^2 = C^2$

$C\approx 3.4\ m$

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Example Question #7 : Pentagons

Find the length of the diagonal of the following pentagon:

Screen_shot_2014-03-11_at_8.34.46_pm

Possible Answers:

$6\sqrt{2}\ m$

$6\ m$

$4\sqrt{3} \ m$

$3\sqrt{2}\ m$

$2\sqrt{3}\ m$

Correct answer:

$3\sqrt{2}\ m$

Explanation:

Use the Pythagorean Theorem to find the length of the diagonal:

$(\frac{1}{2}side)^2+(apothem)^2=(diagonal)^2$

A^2+B^2 = C^2

$(3\ m)^2+(3\ m)^2=C^2$

$C=3\sqrt{2}\ m$

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

What is the side length of a regular pentagon with a perimeter of ?

Possible Answers:

Correct answer:

Explanation:

To find the side length of a regular pentagon with a perimeter of you must use the equation for the perimeter of a pentagon.

The equation is $Perimeter=(side\: length)*(number\: ofsides)$

Plug in the numbers for perimeter and number of sides to get $80=(side\: length)*(5)$

Divide each side of the equation by the number of sides to get the answer for the side length. $\frac{80}{5}=\frac{(side\: length)*(5)}{5}$

The answer is $\frac{80}{5}=16$ .

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Example Question #9 : Pentagons

Find the length of the side of the following pentagon.

Angle_length_of_side_pentagon

The perimeter of the pentagon is $30\ m$ .

Possible Answers:

$6\ m$

$7\ m$

$8\ m$

$5\ m$

$4\ m$

Correct answer:

$6\ m$

Explanation:

The formula for the perimeter of a regular pentagon is

P = 5(s) ,

where represents the length of the side.

Plugging in our values, we get:

$30\ m=5(s)$

$s=6\ m$

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Example Question #10 : Pentagons

Find the length of the side of the following pentagon.

Angle_length_of_side_pentagon

The perimeter of the pentagon is $20\ m$ .

Possible Answers:

$9\ m$

$3\ m$

$4\ m$

$7\ m$

$5\ m$

Correct answer:

$4\ m$

Explanation:

The formula for the perimeter of a regular pentagon is

P = 5(s) ,

where represents the length of the side.

Plugging in our values, we get:

$20\ m = 5(s)$

$s=4\ m$

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High School Math : Pentagons

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Pentagons

Example Question #1 : How To Find An Angle In A Pentagon

Example Question #1 : How To Find An Angle In A Pentagon

Example Question #1 : How To Find An Angle In A Pentagon

Example Question #1 : Pentagons

Example Question #6 : Pentagons

Example Question #7 : Pentagons

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

Example Question #9 : Pentagons

Example Question #10 : Pentagons

All High School Math Resources

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