How to find the area of a pentagon

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Math › How to find the area of a pentagon

Questions 1 - 3

1

Find the area of the following pentagon:

Area_pentagon

$27.5\ m^2$

$28.5\ m^2$

$29.5\ m^2$

$30.5\ m^2$

$26.5\ m^2$

Explanation

The formula for the area of of a pentagon is

$A=\frac{1}{2}5(side)(apothem)$ .

Plugging in our values, we get:

$A=\frac{1}{2}5(4\ m)(2.75\ m)$

$A=27.5\ m^2$

2

Find the area of the following pentagon:

Screen_shot_2014-03-11_at_8.34.46_pm

$45\ m$

$40\ m$

$35\ m$

$50\ m$

$30\ m$

Explanation

The formula for the area of of a pentagon is:

$A=\frac{1}{2}5(side)(apothem)$

Plugging in our values, we get:

$A = \frac{1}{2}5(6\ m)(3\ m)$

$A=45\ m$

3

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

Explanation

The area of a regular polygon can be solved using the following equation: $area=\ \frac{1}{2}(perimeter)(apothem)$ .

To find the perimeterof the pentagon, we multiply the side length by five.

$perimeter=5(side\ length)=5*7=35$

The apothem of a regular polygon ( = number of sides; = side length) is given by the equation below.

$apothem= \frac{s}{2tan(\frac{180}{n})}$

Pluggin in our numbers, we can solve for the apothem.

$apothem==\frac{7}{2tan(\frac{180}{5})}=4.8$

Finally, we can solve for the area.

$area= \frac{1}{2}(35)(4.8)=84$

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