Question

The perimeter of an equilateral triangle is 30 cm.What is it’s area.(A=1/2bh)

Answer 1

Remember that

An equilateral triangle has three equal sides and three equal interior angles.

The measure of each interior angle is 60 degrees

Applying the law of sines

The area of the triangle is equal to

`A=(1)/(2)b^2\cdot\sin (A)`

where

P=3b

P=30 cm ------> given

so

30=3b

b=10 cm

angle A=60 degrees

substitute

`\begin{gathered} A=(1)/(2)\cdot10^2\cdot\sin (60) \\ A=50\cdot\frac{\sqrt[\square]{3}}{2} \\ A=25\sqrt[\square]{3}\text{ cm2} \end{gathered}`