Find the area of the shaded design in the fig | vedclass

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

Question

(A) Let us mark the four unshaded regions as $I, II, III$ and $IV$ (see figure).Area of $I +$ Area of $III = 	ext{Area of square } ABCD - 	ext{Area

Vedclass · Accepted Answer

$57$

Vedclass · Answer

(A) Let us mark the four unshaded regions as $I, II, III$ and $IV$ (see figure).Area of $I +$ Area of $III = 	ext{Area of square } ABCD - 	ext{Area of two semicircles with diameter } 10 \, cm$.Since the side of the square is $10 \, cm$,the radius of each semicircle is $r = 5 \, cm$.Area of $I + III = (10 	imes 10) - 2 	imes (\frac{1}{2} 	imes \pi 	imes 5^2) \, cm^2$$= 100 - (3.14 	imes 25) \, cm^2 = 100 - 78.5 = 21.5 \, cm^2$.Similarly,Area of $II + IV = 21.5 \, cm^2$.Now,the area of the shaded design is the area of the square minus the sum of the areas of the four unshaded regions $(I, II, III, IV)$:Area of shaded design $= 	ext{Area of } ABCD - (	ext{Area of } I + II + III + IV)$$= 100 - (21.5 + 21.5) \, cm^2 = 100 - 43 = 57 \, cm^2$.

Find the area of the shaded design in the figure where $ABCD$ is a square of side $10 \, cm$ and semicircles are drawn with each side of the square as diameter. (in $cm^2$) (Use $\pi = 3.14$)

Similar Questions

Find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles of radii $15 \, cm$ and $18 \, cm$ (in $cm$).

In a circle with radius $20\, cm$,the area of a sector formed by an arc of length $10\, cm$ is ............. $cm^2$.

The maximum area of a triangle inscribed in a semicircle having radius $10 \, cm$ is $\ldots \ldots \ldots \, cm^2$.

In $\odot(O, r)$,the length of minor $\widehat{ACB}$ is one-eighth of the circumference of the circle. Then,the measure of the angle subtended at the centre by that arc is $\ldots \ldots \ldots \ldots$ (in $^\circ$)

In a circular table cover of radius $32 \, cm$,a design is formed by leaving an equilateral triangle $ABC$ in the middle as shown in the figure. Find the area of the design. [Use $\pi = \frac{22}{7}$]

Vedclass Test Series

Exam Paper Generator

Online Exam Module