Find the area of a right-angled triangle if one of the legs is 6 cm and the hypotenuse is 10 cm.

The area of a right-angled triangle is half the product of its legs. S = 1/2 * ab.

1) Find the unknown leg of the triangle.

Knowing the hypotenuse c = 10 cm and one of the legs a = 6 cm of the triangle, we find the second leg according to the Pythagorean theorem. In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. c ^ 2 = a ^ 2 + b ^ 2.

b ^ 2 = c ^ 2 – a ^ 2;

b ^ 2 = 10 ^ 2 – 6 ^ 2 = 100 – 36 = 64;

b = √64 = 8 (cm).

2) Find the area of the triangle.

S = 1/2 * 6 * 8 = 1/2 * 48 = 48/2 = 24 (cm ^ 2).

Answer. 24 cm ^ 2.