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Area of the largest triangle that can be inscribed in a semi-circle of radius $r$ units is

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r^{2}

2 r

4 r

\frac{r}{2}

answer is A.

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Detailed Solution

Given that, radius of semi circle is

r

units and a triangle is inscribed in that circle.
Let

r

be the radius of the circle a point

C

on the circumference of the circle.
Question Image

The base of the triangle is equal to 2r and height of the triangle id equal to

r

.
Evaluate the area of the triangle

△ A B C

A = 12 (2 r) (r) ⇒ A = r 2

The area of the triangle is

r 2

sq. units.
Therefore, the area of largest triangle inscribed a semicircle of radius

r

units is

r^{2}

.
Hence the correct option is 1.

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