Question

The area of an equilateral triangle is $49\sqrt{3}c{m}^2$. Taking each angular point as centre, a circle is described with radius equal to half the length of the side of the triangle as shown in figure. Find the area of the triangle not included in the circle. [Take $\sqrt{3}=1.73$]

• A. $5.67c{m}^2$
• B. $6.12c{m}^2$
• C. $7.77c{m}^2$
• D. $7.98c{m}^2$

Answer 1

The correct option is C $7.77c{m}^2$

Area of equilateral $\Delta ABC=49\sqrt{3}{cm}^2$

$\frac{\sqrt{3}}{4}\times {AB}^2=49\sqrt{3}{cm}^2\Rightarrow {AB}^2=196\Rightarrow AB=\sqrt{196}=14cm$

Now, $\frac{1}{2}AB=AF=FB=BD=DC=CE=EA$

$\therefore$ $AF=FB=BD=DC=CE=EA=7cm$

Now, area of triangle not included $=$ $49\sqrt{3}-3\times \frac{\theta }{{360}^0}\times \pi r^2$

$=$ $49\sqrt{3}-3\times \frac{{60}^0}{{360}^0}\times \pi r^2$

$=49$$\times$$1.73-77$

$=84.77-77$

$=7.77$ ${cm}^2$