Area of the largest triangle that can be inscribed in a semicircle of radius r units is

Here, we need to find the area of the largest triangle that can be inscribed in a semicircle of radius

r

units.
Let ABC be the triangle.

The area of a triangle is equal to the base times the height.
In a semicircle, the diameter is the base of the semi-circle.
Base =

2 \times r

(r = the radius)
If the triangle is an isosceles triangle with an angle of

45^{\circ}

at each end, then the height of the triangle is also a radius of the circle.
We know that,
A =

\frac{1}{2} \times b \times h

Here,

b = 2 r

h = r

Then,
A =

\frac{1}{2} \times 2 r \times r

A =

r^{2}

Hence, the area of the largest triangle that can be inscribed in a semicircle of radius

r

units is

r^{2}

sq. units.
Therefore, option 1 is correct.

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