The side of an isosceles triangle is 35 and the base is 42. Find the area of the triangle.

1) What is the half-perimeter of this triangle?

p = (35 + 35 + 42) / 2 = 112/2 = 56.

2) What is the area of this triangle?

We find the area of the triangle by Heron’s formula, we have

S = √ (p * (p – a) ^ 2 * (p – c)) = √ (56 * (56 – 35) ^ 2 * (56 – 42)) = √ (7 * 8 * 21 ^ 2 * 14) = √ (7 * 8 * 21 ^ 2 * 2 * 7) = √ (7 ^ 2 * 21 ^ 2 * 16) = 7 * 21 * 4 = 588.

Answer: the area of the triangle is 588.