The area of the largest triangle that can be inscribed in a semicircle of radius r unit is;

A) r

^{2}sq. u B)1/2 r^{2}sq. u(C) 2r

^{2 }sq. u (D) root2 r^{2}sq. u

**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 degrees 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:

This is equal to 2*r (r = the radius)

If the triangle is an isosceles triangle with an angle of 45 degrees 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

Since the area of the triangle is equal to (1/2)*b*h, and the base remains the same while the height of the triangle is less at any other point on the surface of the semi-circle, then the largest area is when the height equals the radius of the triangle.

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

Since the area of the triangle is equal to (1/2)*b*h, and the base remains the same while the height of the triangle is less at any other point on the surface of the semi-circle, then the largest area is when the height equals the radius of the triangle.

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