Question

Find the area of the largest triangle that can be inscribed in a semi circle of radius r unit

Answer 1

The area of a triangle is 1/2 x b x h.
When you put a triangle in a semicircle, the greatest height it can have is the radius and the greatest lenght of the base it can have would be the diameter.

(Sorry, It's a bit hard to explain w/out a diagram)


Anyways, the area of the triangle would be 1/2 x r x d (where r is the radius and d is the diameter).

We can simplify this further: Since the diameter is twice the radius, the area would now be 1/2 x r x 2r

= 1/2 x $2r^{2}$  = $\frac{ 2r^{2} }{2}$

The 2's get canceled out so the area = $r^{2}$

Answer 2

Answer:

= r^2

Step-by-step explanation:

The base of the triangle will be diameter means 2r

And the height of the triangle will be r.

Area of triangle = 1/2 × base × height

= 1/2 × 2r × r

= r^2