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

#### Options

r

^{2 }sq.units`1/2` r

^{2 }sq.units2 r

^{2 }sq.units`sqrt(2)` r

^{2 }sq.units

#### Solution

Area of the largest triangle that can be inscribed in a semi-circle of radius r units is **r ^{2 }sq.units**.

**Explanation:**

The largest triangle that can be inscribed in a semi-circle of radius r units is the triangle having its base as the diameter of the semi-circle and the two other sides are taken by considering a point C on the circumference of the semi-circle and joining it by the endpoints of diameter A and B.

∴ ∠ C = 90° .....(By the properties of circle)

So, ΔABC is right-angled triangle with base as diameter AB of the circle and height be CD.

Height of the triangle = r

∴ Area of largest ΔABC = `1/2`× Base × Height

= `1/2` × AB × CD

= `1/2` × 2r × r

= r^{2} sq.units