PS is a diameter of a circle of radius 6 cm. Q and R are points on the diameter that PQ, QR and RS are equal. Semicircles are drawn with PQ and QS as diameters, as shown in the figure. Find the perimeter and the area of the shaded region.(π = 3.14.)
Also find the area of the shaded region.
Answers
Area of shaded region = 37.68 cm²
Perimeter of shaded region = 37.68 cm
Explanation:
Given: Radius of circle = 12 cm. PQ, QR and RS are equal. Semi circles are drawn on PQ and QS as diameters.
To find: Perimeter and area of the shaded region.
PS = diameter = 2 * 6 = 12 cm
We know that PQ = QR = RS = 1/3 * PS= 1/3 * 12 = 4 cm.
QS = 2*PQ = 8 cm
Radius of circle with PS a diameter = 6 cm
Radius of circle with PQ a diameter = 2 cm
Radius of circle with QS a diameter = 4 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
= 1/2 [ 3.14 x 6² + 3.14 x 2² - 3.14 x 4² ]----------------as area = 1/2
= 1/2 [ 3.14 x 36 + 3.14 x 4 – 3.14 x 16 ]
= 1/2[ 3.14 ( 36 + 4 – 16)]
= 1/2 ( 3.14 x 24 ) = 12 * 3.14 = 37.68
Area of shaded region = 37.68 cm²
Perimeter of shaded region = Perimeter of semicircle with PS as diameter + Perimeter of semicircle with PQ as diameter + area of semicircle with QS as diameter = 1/2 (2*3.14) [6 + 2 + 4] = 12* 3.14 = 37.68 cm