Multiple choice

$\triangle ABC$ is a right triangle, the radius of its circumcircle is $3\ cm$ and the length of its altitude drawn from the opposite vertex to the hyptotenuse is $2\ cm$. Then the area of the triangle is

  1. $12\ sq. cm$
  2. $3\ sq. cm$
  3. $6\ sq. cm$
  4. $5\ sq. cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For a right triangle, the hypotenuse is twice the circumradius, so its length is 6 cm. The area is 1/2 x hypotenuse x altitude to the hypotenuse = 1/2 x 6 x 2 = 6 square centimetres.

AI explanation

In a right triangle, the hypotenuse is the diameter of the circumcircle, making the hypotenuse 2 * 3 cm = 6 cm. The area of a triangle is calculated as half of the base times the height. Using the hypotenuse as the base and the given altitude of 2 cm, the area is 0.5 * 6 * 2 = 6 sq cm.

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