Multiple choice

What is the area of a right angled triangle if the radius of its circumcircle is 3 cm and altitude drawn to the hypotenuse is 2 cm?

  1. $\displaystyle 4\sqrt{3}cm^{2}$
  2. 6 $\displaystyle cm^{2}$
  3. 7 $\displaystyle cm^{2}$

  4. <span class="MathJax_Preview"><span class="MathJax"><span class="math"><span class="mrow"><span class="mstyle"><span class="mrow"><span class="mi">5 c<span class="msubsup"><span class="mi">m<span class="texatom"><span class="mrow"><span class="mn">2<span class="MJX_Assistive_MathML">cm2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a right triangle, the circumradius R = hypotenuse / 2. So hypotenuse = 2 * 3 = 6 cm. The area of a triangle is 1/2 * base * height. Using the hypotenuse as the base and the given altitude as the height, Area = 1/2 * 6 * 2 = 6 cm^2.

AI explanation

In a right angled triangle, the hypotenuse is the diameter of its circumcircle, so the hypotenuse is 2 times 3 = 6 cm. The area of a triangle is half the product of its base and height. Therefore, the area is 0.5 times 6 times 2 = 6 cm^2.

Keep practicing — related questions