Question

step by step explanation....

class 10.....

Answer 1

Given :
AB = 6 cm , AC = 8 cm
Diameter AB = 6 cm
Diameter  AC = 8 cm

In right angled ∆ABC,
BC² = AB² + AC² [by Pythagoras theorem]
BC² = 6² + 8²
BC² = 36 +64 = 100
BC = √ 100 = 10
BC= 10 cm

Area of semicircle = ½(πr²)

Area of semicircle with AB as diameter = ½(π) (6/2)²= 1/2π (3)² = 9π/2 cm²
Area of semicircle with AC as diameter = ½(π) (8/2)²= 1/2π (4)² = 1/2π (16) =8π cm²

Area of ∆ABC = ½ × AC × AB = 1/2× 8 ×6 = 4×6 =24 cm²

Area of semicircle with BC as diameter= ½(π) (10/2)²= 1/2π (5)² = 1/2π (25) =25π/2 cm²

Area of shaded region= Area of semicircle with AB as diameter + Area of semicircle with AC as diameter + Area of ∆ABC - Area of semicircle with BC as diameter

= 9π/2 + 8π + 24 - 25π/2
= 9π/2 + 8π - 25π/2+ (24)
= π(9/2 +8 -25/2) + 24
= π(4.5 - 12.5 +8) +24
= π (-8 +8) + 24
= π (0)+24

= 0 + 24 = 24
Area of shaded region= 24 cm²

Hence, the Area of shaded region = 24 cm²

HOPE THIS WILL HELP YOU.

Answer 2

Please see the attachment