Question

In the given figure, find the perimeter of the shaded region where ADC, AEB and BFC are semi circle on diameter AC,AB and BC respectively.

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

HOPE THIS WILL HELP YOU...

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Perimeter of shaded region is AEBFCDA = arc(AEB) + arc(BFC) + arc(CDA)

= π(AB)/2 + π(BC)/2 + π(AC)/2

Where AB, BC and AC are diameters of the different circles.

Also we know Semi-perimeter of a circle is π × diameter/2

Perimeter of shaded region = π × 2.8/2 + π × 1.4/2 + π × (2.8 + 1.4)/2

Perimeter of shaded region = π/2 × 8.4

Perimeter of shaded region = π × 4.2

Perimeter of shaded region = 22/7 × 4.2

Perimeter of shaded region = 13.2 cm

Hence, The perimeter of the shaded region is 13.2 cm.