Question

There is a circle of radius 10 units that circumscribes an equilateral triangle. A quadrilateral is drawn by joining mid-points of two adjacent sides of the triangle. Find the area of the quadrilateral

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

In an equilateral triangle circum radius = $\frac{2}{3}$ h,

10 = $\frac{2}{3}$ * $\frac{\sqrt{3}}{2}S$

Side = 10\(\sqrt 3\) units.

Area of Triangle = $\frac{\sqrt{3}}{4}(10\sqrt{3}{)}^2$

By graphical division, we need $\frac{3}{4}$${}^{th}$ of the area of the triangle =$\frac{3}{4}\times \frac{\sqrt{3}}{4}\times (10\sqrt{3}{)}^2$ = $\frac{225\sqrt{3}}{4}$