Question

A circle inscribed in a triangle whose side are 6m 10m 8m then the area of circle

Answer 1

$since \: we \: know \: \\ area = \: \: semi \: circumference \: \times \: inradius \\ 24 \: = 12 \times r \\ r = 2 \\ so \: the \: area \: is \: \pi {2}^{2} \\ \\ i \: \: wish \: yo \: get \: your \: ans.$

Answer 2

*See attached diagram

The sides are 6m, 10cm and 8cm (Given)

Check if it is a right angle triangle:

a² + b² = 6² + 10²

a² + b² = 100

√100 = 10 = c

⇒ Hence the triangle is a right angle triangle

Find the area of the big triangle:

Area = 1/2 x base x height

Area = 1/2 x 6 x 8 = 24 m²

Find the area of the 3 small triangle:

Split the triangles as indicated by the picture, radius being the height of all the 3 triangles.

Area of Δ BOC = 1/2 x 6 x r = 3r

Area of Δ AOB = 1/2 x 8 x r = 4r

Area of Δ AOC = 1/2 x 10 x r = 5r

Total area = 3r + 4r + 5r = 12r

Solve r:

12r = 24 m³

r = 24 ÷ 12 = 2 m

Find the area of the circle:

Area of the circle = πr²

Area of the circle = π(2)² = 4π = 12.57 m²

Answer: Area of the circle = 12.57 m²