### What is the area of the largest triangle that can be inscribed in a semi-circle of radius $r$ units?

$r^2 \text { sq. units }$

Step by Step Explanation:
1. The largest triangle that can be inscribed in a semi-circle with the center $O$ will be a right-angled isosceles triangle, $ABC$ with $OA = OB = OC$ and $OC \perp AB$.

Let us draw the triangle $ABC$ inside the semi-circle.

2. We see that the length of the base of the triangle is equal to the diameter of the circle.

The radius of the circle = $r$
So, the base of the triangle = $2r$

Also, the height of the triangle = $r$

Thus, the area enclosed by the triangle = $\dfrac { 1 } { 2 } \times Base \times Height = \dfrac { 1 } { 2 } \times 2r \times r = r^2 \text { sq. units. }$

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