Multiple choice

The area of the largest triangle that can be in-scribed in a semi circle whose radius is r cm is

  1. $ \displaystyle 2r$ $ \displaystyle cm^{2}$
  2. $ \displaystyle r^{2}$ $ \displaystyle cm^{2}$
  3. $ \displaystyle 2r^{2}$ $ \displaystyle cm^{2}$
  4. $ \displaystyle \frac{1}{4}r^{2}$ $ \displaystyle cm^{2}$
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B Correct answer
Explanation

The base of the triangle is the diameter of the semicircle (2r) and the height is the radius (r). Area = (1/2) * base * height = (1/2) * 2r * r = r^2.

AI explanation

The largest triangle inscribed in a semicircle of radius r has a base of 2r and a height of r. Using the triangle area formula, Area = 0.5 x base x height = 0.5 x 2r x r = r^2. The result is r^2 cm^2.

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