Question

The area of the largest triangle that can be inscribed in a semicircle of radius r is (A) 2r cm2 (B) r 2 cm2 (C) r cm2 (D) √r cm2​

Answer 1

Answer:

1. The area of a triangle is equal to the base times the height.

In a semi circle, the diameter is the base of the semi-circle.

This is equal to 2×r (r = the radius)

If the triangle is an isosceles triangle with an angle of 45 degree  at each end, then the height of the triangle is also a radius of the circle.

A = 1/2 ×b×h formula for the area of a triangle becomes

A = 1/2 ×2×r×r because:

The base of the triangle is equal to 2×r

The height of the triangle is equal to r

A = 1/2 ×2×r×r becomes:

A = r ^2

Hence the correct answer is b) r^2 cm^2

Refer attachment below: