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


Answer:

r2 sq. units 

Step by Step Explanation:
  1. The largest triangle that can be inscribed in a semi-circle with the center O will be a right-angled isosceles triangle, ABC with OA=OB=OC and OCAB.

    Let us draw the triangle ABC inside the semi-circle.
    C A O B

  2. We see that the length of the base of the triangle is equal to the diameter of the circle.

    The radius of the circle = r
    So, the base of the triangle = 2r

    Also, the height of the triangle = r

    Thus, the area enclosed by the triangle = 12×Base×Height=12×2r×r=r2 sq. units. 

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