Question

the area of a circle is inscribed in a right angle triangle with sides of length 8 cm 15 cm and 17 cm is

Answer 1

Answer:

The area of a circle is inscribed in a right angle triangle = 28.28 cm square

Step-by-step explanation:

It is given that

A right angle triangle with sides of length 8 cm 15 cm and 17 cm

Base = 8cm

Height = 15 cm

Hypotenuse = 17 cm

To find the area of triangle

Area, A = 1/2 Base x height = 1/2 x 8 x 15 = 60 cm square

From the figure attached with this figure, triangle ABC is a right triangle with a circle  inscribed with radius r

To find radius r

Area of triangle ABC = Ar(AOC) + Ar(AOB) + Ar(BOC)

Here height of  all triangle = r

Area, A = (1/2 x AC x r) + (1/2 x AB x r) + (1/2 x BC x r) = 60

1/2 x r [8 + 15 + 17] = 60

20r = 60

r= 3cm

To find area of circle

Area of circle = πr^2 = 3.14 x 3 x 3 = 28.28 cm square