Question

A regular decagon with a radius of 15 the length of one side measures 9.3 units. What is the approximate area of the regular decagon rounded to the nearest tenth ?

Answer 1

The approximate area of the regular decagon rounded to the nearest tenth will be 663.4 square units.

Step-by-step explanation

Radius
`(r)` of the regular decagon is 15 units and the length of one side
`(s)` is 9.3 units.

Formula for the Area of regular decagon
`=(1)/(2)* Perimeter * Apothem`

Formula for finding the length of apothem
`(a)= r*sin(72)`

So, the length of apothem will be:
`15sin(72)` units

and the perimeter will be:
`10s= 10*9.3=93` units

Thus, the area of the regular decagon
`=(1)/(2)* 93 * 15sin(72)=663.361.... \approx 663.4` square units.