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

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 . 225√32

B . 225√34

C . 225√38

D . 225√312

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\(\sqrt3\) units.
Area of Triangle =

\frac{\sqrt{3}}{4} (10 \sqrt{3})^{2}

There Is A Circle Of Radius 10 Units That Circumscribes An...

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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