Question

In the following figure , abc is a right angles triangle at A find the area of the shaded region if AB is 6 cms and BC is 10 cms and l is the centre of the circle of ABC triangle

Answer 1

Answer:

11.36cm²

Step-by-step explanation:

In ΔABC,

By Pythagoras theorem,

BC² = AB² + AC²

100 = 36 + AC²

AC² = 64

⇒ AC = 8cm

Area of ΔABC = 1/2 × 6 × 8

                       = 24cm²

For finding the radius of the circle, we have a formula for incircle (Since its inside the circle)

(A+B-H)

-----------              (H → Hypotenuse)

    2

Hence, r = (6 + 8 - 10) ÷ 2

           ⇒ r = 2cm

Area of circle = πr²

                      = 3.16 × 4

                      = 12.64

∴ Area of the shaded region = Area of Δle - Area of circle

                                               = 24 - 12.64

                                               = 11.36cm²

Good luck <3