There is a circle of radius 10 units that circumscribes an equilateral triangl

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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

Options:

A .

\frac{225 \sqrt{3}}{2}

B .

\frac{225 \sqrt{3}}{4}

C .

\frac{225 \sqrt{3}}{8}

D .

\frac{225 \sqrt{3}}{12}

Answer: Option B
:
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 $\frac{3}{4}$ $^{t h}$ of the area of the triangle = $\frac{3}{4} \times \frac{\sqrt{3}}{4} \times (10 \sqrt{3})^{2}$ = $\frac{225 \sqrt{3}}{4}$

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