The leg of a right-angled triangle is 9 and the hypotenuse is 11, find the area.

By condition, △ ABC is given: ∠C = 90˚, AC = 9 and BC – legs, AB = 11 – hypotenuse (since it lies opposite the right angle).

The area of ​​a triangle is found as half the product of its side and the height drawn to this side. Since the legs in a right-angled triangle are its heights, its area is found as half the product of its legs, that is:

S = (a * b) / 2,

where a and b are the legs of a right-angled triangle.

By the Pythagorean theorem, we find the length of the leg BC:

BC = √ (AB² – AC²) = √ (11² – 9²) = √ (121 – 81) = √40 = √ (4 * 10) = 2√10.

Find the area △ ABC:

S = (AC * BC) / 2 = (9 * 2√10) / 2 = 18√10 / 2 = 9√10.

Answer: S = 9√10.