Question

Pqrs is a diameter of circle of radius 6cm. The lengths pq, qr, and rs are equal. Semicircle are drawn with pq and qs as diameter as shown in the given figure. If PS =12cm,find the perimeter and area of the shaded region take π=3.14

Answer 1

Hello,
observing the figure.
we have that:
PS=12 CM
as
PQ=QR=RS=1/3×PS=1/3×12=4 cm
and
QS=2PQ
QS=2×4=8 cm

we calculate the area of shaded region:
A= area of semicircle with PS as diameter + area of semicircle with PQ as diameter – area of semicircle with qs as diameter;
= 1/2 [ 3.14 x 6² + 3.14 × 2² - 3.14 × 4² ];
= 1/2 [ 3.14 ×36 + 3.14 ×4 – 3.14 ×16 ] ;
= 1/2[ 3.14 ( 36 + 4 – 16)];
= 1/2 ( 3.14 × 24 );
 = 1/2 × 75.36 ;
=37.68 cm²

The  area of shaded region = 37.68 cm².

we calcutate the perimeter of shaded region:
P=πr= 12×22/7 =264/7 

bye :-)

Answer 2

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PS = 12 cm (6+6)
As PQ = QR = RS

➧ PQ = QR = RS
➾ 1/3 × PS
➾ 1/3 × 12
➾ 4 cm

QS = 2 PQ
QS = 2 × 4
   = 8 cm

➧ Area of shaded region =
Area of semicircle with PS as diameter + Area of semicircle with PQ as diameter - Area of semicircle with QS as diameter.

➾ ½ [3.14 × 6² + 3.14 × 2² - 3.14 × 4²]

➾ ½ [3.14 × 36 + 3.14 × 4 - 3.14 × 16]

➾ ½ [3.14 (36 + 4 - 16)]

➾ ½ (3.14 × 24) = ½ × 75.36

➧ Area of shaded region,
➾ 37.68 cm²

➧ Perimeter 0f shaded region,
➾ 12 × 22 / 7
➾ 264 / 7
➾ 37.68 cm²...✔

_________
Thanks...✊