In the figure,arcs are drawn by taking vertic | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given that $ABC$ is an equilateral triangle with side length $10 \, cm$.Therefore,$\angle A = \angle B = \angle C = 60^{\circ}$.Since $D, E$ and $

Vedclass · Accepted Answer

$39.25$

Vedclass · Answer

(D) Given that $ABC$ is an equilateral triangle with side length $10 \, cm$.Therefore,$\angle A = \angle B = \angle C = 60^{\circ}$.Since $D, E$ and $F$ are mid-points of sides $BC, CA$ and $AB$ respectively,the radius of each arc is $r = 5 \, cm$.The shaded region consists of three sectors,each with a central angle of $60^{\circ}$ and radius $r = 5 \, cm$.Area of one sector $= \frac{	heta}{360^{\circ}} 	imes \pi r^2 = \frac{60^{\circ}}{360^{circ}} 	imes 3.14 	imes (5)^2$.Area of one sector $= \frac{1}{6} 	imes 3.14 	imes 25 = \frac{78.5}{6} \approx 13.0833 \, cm^2$.Total area of the shaded region $= 3 	imes (	ext{Area of one sector}) = 3 	imes \frac{78.5}{6} = \frac{78.5}{2} = 39.25 \, cm^2$.

In the figure,arcs are drawn by taking vertices $A, B$ and $C$ of an equilateral triangle of side $10 \, cm$ as centers to intersect the sides $BC, CA$ and $AB$ at their respective mid-points $D, E$ and $F$. Find the area of the shaded region (Use $\pi = 3.14$) (in $cm^2$).

Similar Questions

The length of the minute hand of a clock is $10.5 \, cm$. Find the area of the region swept by it between $2.25 \, PM$ and $2.40 \, PM$. (in $cm^2$)

If the perimeter of a circle is equal to that of a square,then the ratio of their areas is

In a circle,the ratio of the areas of two distinct minor sectors is $1:4$. Then,the ratio of the angles at the centre for those minor sectors is $\ldots \ldots \ldots \ldots$.

Is the area of the largest circle that can be drawn inside a rectangle of length $a \, cm$ and breadth $b \, cm$ $(a > b)$ equal to $\pi b^{2} \, cm^{2}$? Why?

The radius of a field in the shape of a sector is $50 \, m$. The cost of fencing its boundary is ₹ $5400$ at the rate of ₹ $30 / m$. Find the cost of tilling at the rate of ₹ $15 / m^2$. (in ₹)

Vedclass Test Series

Exam Paper Generator

Online Exam Module