Question

In the figure, find teh perimeter of the shaded region where. ADC, AEB and BFC are semi-circles on diameters AC, AB and BC respectively.

Answer 1

Perimeter of shaded region is 13.2 cm

Text Solution ::

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= \([ \pi\times1.4) +(\pi \times0.7)+(\pi\times2.1)] \)cm
= \(\pi(1.4+0.7+2.1) \)cm
=( 22/7) \(\times\)4.2
= 22\(\times\).6
= 13.2 cm
Hence, the perimeter of the shaded region is 13.2 cm

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