Question

An equilateral triangle has a perimeter of 48 cm. What is the area?

Answer 1

`A=64√(3)\ cm^2`

Explanation:

we know that

An equilateral triangle has three equal sides and three equal interior angles (each interior angle measure 60 degrees)

so

The perimeter is equal to

`P=3b`

where

b is the length side of the equilateral triangle

we have

`P=48\ cm`

substitute

`48=3b`

solve for b

`b=48/3\\b=16\ cm`

Find the area

The formula of area applying the law of sines is equal to

`A=(1)/(2)b^2sin(60^o)`

substitute the value of b

`A=(1)/(2)(16)^2sin(60^o)`

`sin(60^o)=(√(3))/(2)`

`A=(1)/(2)(16)^2((√(3))/(2))`

`A=64√(3)\ cm^2`