Question

76 cm a 52 cm Find the area of the regular pentagon (the answer has one digit after the decimal point)​

Answer 1

98.8 cm²

Explanation:

Hi there!

`A=(1)/(2) Pa` where P is the perimeter of the pentagon and a is the apothem (the line going from the center of the pentagon one edge)

1) Find the perimeter

`P=5l` where l is the side length

Plug in the side length 7.6 cm

`P=5(7.6)\\P=38`

Therefore, the perimeter of the pentagon is 38 cm.

2) Find the area

`A=(1)/(2) Pa`

Plug in the perimeter (38) and the apothem (5.2)

`A=(1)/(2) (38)(5.2)\\A=(1)/(2) (38)(5.2)\\A=(1)/(2) (197.6)\\A=98.8`

Therefore, the area of the pentagon is 98.8 cm².

I hope this helps!