In a right-angled triangle, the hypotenuse is 26, and one of the legs is 10. Find the area of the triangle.

In order to find the area of a given triangle, it is most convenient to use Heron’s formula:

S = √ (p (p – a) (p-b) (p-c)), where:

S is the area of the triangle;

p – half-perimeter of a triangle

(p = (a + b + c) / 2);

a, b, c – sides of the triangle.

But to calculate the area, we need to calculate the length of the second leg. To do this, apply the Pythagorean theorem:

AB² = BC² + AC²;

BC² = AB² – AC²;

ВС² = 26² – 10² = 676 – 100 = 576;

BC = √576 = 24 cm.

p = (26 + 10 + 24) / 2 = 60/2 = 30 cm;

S = √30 • (30 – 26) • (30 – 10) • (30 – 24) = √30 • 4 • 20 • 6 = √14400 = 120 cm².

Answer: the area of the triangle is 120 cm².