# Find the area of the triangle, one of the legs is 6cm, and the hypotenuse is 10cm.

September 13, 2021 | education

| Let AC and BC be the legs of a right-angled triangle.

AB – hypotenuse.

Let’s use the Pythagorean theorem.

By the Pythagorean theorem: AB ^ 2 = AC ^ 2 + BC ^ 2;

10 ^ 2 = 6 ^ 2 + BC ^ 2;

100 = 36 + BC ^ 2;

BC ^ 2 = 64;

BC = √64;

BC = 8.

S∆ABC = (AC * BC) / 2 = (6 * 8) / 2 = 24 cm2.

Answer: S∆ABC = 24 cm2.

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