Question

What is the area of a Reuleaux triangle that has a diameter of 18.6 m? Round your answer to the nearest tenth.

Answer 1

The Reuleaux triangle is shown in the attached figure

we know that

the area of a Reuleaux triangle is equal to

$A=\frac{1}{2} *(\pi -\sqrt{3} )*r^{2}$

where

r=18.6/2--------> r=9.3 m

so

$A=\frac{1}{2} *(\pi -\sqrt{3} )*9.3^{2}$

$A=60.96$

therefore

the answer is

61 m²