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

The largest triangle that can be inscribed in a semi-circle is a right-angled triangle, where the hypotenuse is the diameter of the semi-circle.

Step 1: Identify the given The radius of the semi-circle is given as r units.

Step 2: Calculate the diameter The diameter of the semi-circle is twice the radius. So, the diameter = 2r.

Step 3: Identify the sides of the triangle In the right-angled triangle, the hypotenuse is the diameter of the semi-circle (2r), and the two other sides are perpendicular to each other. Let's call these sides a and b.

Step 4: Calculate the area of the triangle The area of a right-angled triangle is given by the formula 1/2 * base * height. Here, we can consider one of the sides (a or b) as the base and the other as the height. However, in the largest triangle that can be inscribed in a semi-circle, the base and height are equal to the radius of the semi-circle (r).

So, the area of the triangle = 1/2 * r * r = 1/2 * r^2 square units.