Question

1. Find the radius of the incircle of ΔABC, AB = 7 cm, BC = 24 cm and ∠B = 90°.
2. Find the shaded area. [Take π = 3.14]

Answer 1

i. Find the radius of the incircle of ΔABC, where AB = 7 cm, BC = 24 cm and ∠B = 90°.

Given:

• AB = 7 cm
• BC = 24 cm
• ∠B = 90°

Step 1: Calculate the hypotenuse AC using Pythagoras theorem:

`AC = sqrt(AB^2 + BC^2)`

= `sqrt(7^2 + 24^2)`

= `sqrt(49 + 576)`

= `sqrt(625)`

= 25 cm

Step 2: Calculate the semi-perimeter (s) of the triangle:

`s = (AB + BC + AC)/2`

= `(7 + 24 + 25)/2`

= `56/2`

= 28 cm

Step 3: Calculate the area of the triangle:

`Area = 1/2 xx AB xx BC`

= `1/2 xx 7 xx 24`

= 84 cm²

Step 4: Calculate the radius (r) of the incircle using formula:

`r = ("Area of"  Δ)/"Semi-perimeter"`

= `84/28`

= 3 cm

The radius of the incircle is 3 cm.

ii. Find the shaded area of the triangle minus area of the incircle. Take π = 3.14.

Step 1: Calculate the area of the incircle:

Area of incircle = πr²

= 3.14 × 3²

= 3.14 × 9

= 28.26 cm²

Step 2: Calculate the shaded area:

Shaded area = Area of Δ – Area of incircle

= 84 – 28.26

= 55.74 cm²

The shaded area is 55.74 cm².