How to find the area of a pentagon - High School Math

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Question

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

Answer

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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Question

Find the area of the following pentagon:

Answer

The formula for the area of of a pentagon is

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

Plugging in our values, we get:

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

$A=27.5\ m^2$

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Question

Find the area of the following pentagon:

Answer

The formula for the area of of a pentagon is:

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

Plugging in our values, we get:

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

$A=45\ m$

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