What is the area of the largest triangle that can be inscribed in a semi-circle of radius rr units?
Answer:
r2 sq. units r2 sq. units
- The largest triangle that can be inscribed in a semi-circle with the center OO will be a right-angled isosceles triangle, ABCABC with OA=OB=OCOA=OB=OC and OC⊥ABOC⊥AB.
Let us draw the triangle ABCABC inside the semi-circle.
- We see that the length of the base of the triangle is equal to the diameter of the circle.
The radius of the circle = rr
So, the base of the triangle = 2r2r
Also, the height of the triangle = rr
Thus, the area enclosed by the triangle = 12×Base×Height=12×2r×r=r2 sq. units. 12×Base×Height=12×2r×r=r2 sq. units.