The area of an equilateral triangle ABC is 17 | vedclass

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Question

(C) Let the side of the equilateral triangle be $a$.Area of equilateral triangle $= 17320.5 \, cm^2$.$\frac{\sqrt{3}}{4} a^2 = 17320.5$$\frac{1.73205}

Vedclass · Accepted Answer

$1620.5$

Vedclass · Answer

(C) Let the side of the equilateral triangle be $a$.Area of equilateral triangle $= 17320.5 \, cm^2$.$\frac{\sqrt{3}}{4} a^2 = 17320.5$$\frac{1.73205}{4} a^2 = 17320.5$$a^2 = 4 	imes 10000 = 40000$$a = 200 \, cm$.The radius of each circle is $r = \frac{a}{2} = \frac{200}{2} = 100 \, cm$.Each interior angle of an equilateral triangle is $60^{\circ}$.Area of one sector $= \frac{60^{\circ}}{360^{\circ}} 	imes \pi r^2 = \frac{1}{6} 	imes 3.14 	imes (100)^2 = \frac{31400}{6} = \frac{15700}{3} \, cm^2$.Area of three sectors $= 3 	imes \frac{15700}{3} = 15700 \, cm^2$.Area of the shaded region $=$ Area of equilateral triangle $-$ Area of three sectors$= 17320.5 - 15700 = 1620.5 \, cm^2$.

The area of an equilateral triangle $ABC$ is $17320.5 \, cm^2$. With each vertex of the triangle as a centre,a circle is drawn with a radius equal to half the length of the side of the triangle (see figure). Find the area of the shaded region in $cm^2$. (Use $\pi = 3.14$ and $\sqrt{3} = 1.73205$)

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