Question

In the figure, an equilateral triangle of side 6 cm and its circumcircle is shown. Find the area of shaded portion. Take $(\pi =3.14,\sqrt{3}=1.73)$

• A. $22.11c{m}^2$
• B. $22c{m}^2$
• C. $21.11c{m}^2$
• D. $23.11c{m}^2$

Answer 1

The correct option is A $22.11c{m}^2$

Area of the equilateral triangle=$\frac{\sqrt{3}}{4}{a}^2$
=$\frac{1.73}{4}(6{)}^{2}c{m}^2$
=$15.57c{m}^2$
Radius r of the circumscribing circle =$\frac{a}{\sqrt{3}}$
=$\frac{6}{1.73}$
=$3.47cm$
Area of the circle $=\pi r^2$
$=3.14\times (3.47{)}^2$
$=37.68c{m}^2$
Area of shaded region =Area of the circle-Area of the triangle
$=(37.68-15.57)c{m}^2$
$=22.11c{m}^2$