Question

in the figure if ab is equals to 16 cm and BC is equals to 12 centimetre calculate the area of the shaded region in the figure​

Answer 1

Answer:

140 cm²

Step-by-step explanation:

Assuming few things to answer like

AC is Diameter   & ΔABC is right angle triangle & small arc with Radius = 12 cm

Then Area of Shaded Region

= Area of Δ ABC + Area of Semi circle with Dia AC - Arc Area with Radius 12 cm

AC² = AB² + BC²

=> AC² = 16² + 12²

=> AC² = 256 + 144

=> AC² = 400

=> AC = 20 cm

Area of Δ ABC = (1/2) * AB * BC  = (1/2) * 16 * 12  = 96 cm²

Area of Semi circle with Dia AC (20 cm)  =  (1/2)πr² = (1/2)π (10)² = 50π cm²

Arc Area with Radius 12 cm = (90/360)πr² = (1/4)π 12² = 36π cm²

area of the shaded region in the figure = 96 + 50π - 36π

= 96 + 14π cm²

Using π = 22/7

= 96 + 14*(22/7)

= 96 + 44

= 140 cm²