Question 239336
I believe the solution is going to be A (r^2 squared units).


The area of a triangle is equal to the base times the height.


In a semi circle, the diameter is the base of the semi-circle.


This is equal to 2*r (r = the radius)


If the triangle is an isosceles triangle with an angle of 45 degrees at each end, then the height of the triangle is also a radius of the circle.


A = (1/2)*b*h formula for the area of a triangle becomes:


A = (1/2)*2*r*r because:


The base of the triangle is equal to 2*r
The height of the triangle is equal to r


A = (1/2)*2*r*r becomes:


A = r^2


Since the area of the triangle is equal to (1/2)*b*h, and the base remains the same while the height of the triangle is less at any other point on the surface of the semi-circle, then the largest area is when the height equals the radius of the triangle.


Your answer is selection A.