Chapter 13.3, Problem 53SR

To determine

To calculate:

The area of shaded region of given figure.

Answer to Problem 53SR

The area of shaded region is $27\sqrt{3}c{m}^2$ .

Explanation of Solution

Given information:

  

Calculation:

A shaded circle with the dimeter $12cm$ contains an un-shaded triangle with three side lengths of $6\sqrt{3}cm$ .

Since, the triangle can be split into two right tringles with a base length of $6\sqrt{3}cm$ and a hypotenuse of $6\sqrt{3}cm$ , the height of each right triangle is equal to $3\sqrt{3}\times 3\sqrt{3}=9cm$ .

Therefore, the area of the entire un-shaded triangle is equal to,

  $\frac{1}{2}\left(6\sqrt{3}cm\right)\left(9cm\right)=27\sqrt{3}c{m}^2$

Hence the area of shaded region is $27\sqrt{3}c{m}^2$ .