Question

38. In the given figure, find the area and perimeter of the shaded region, where
semi-circles on diameters AC,BC,AB respectively
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Answer 1

[FIGURE IS IN THE ATTACHMENT]

Given:

Diameter of semicircle AEB= 2.8 cm

RADIUS OF SEMICIRCLE(AEB)= 2.8/2= 1.4 cm

Diameter of semicircle BFC=1.4 cm

RADIUS OF SEMICIRCLE(BFC)= 1.4/2= 0.7 cm

Diameter of semicircle ADC= 2.8+1.4 = 4.2 cm

RADIUS OF SEMICIRCLE(ADC) = 4.2/2= 2.1 cm.

Perimeter of the shaded region= sum of the arc of semicircle AEB, BFC and ADC= [π×1.4) +(π×0.7)+(π×2.1)] cm

= π(1.4+0.7+2.1) cm

=( 22/7) ×4.2

= 22× .6

= 13.2 cm

Hence, the perimeter of the shaded region is 13.2 cm