Heron’s formula gives a method of finding the area of a triangle if the lengths of its sides are known. Suppose that a, b, and c are the lengths of the sides. Let s denote one-half of the perimeter of the triangle (called the semiperimeter)—that is,

Then the area of the triangle is given by

Use Heron’s formula to solve each problem.

Find the area of a triangle with sides of lengths a = 20 ft, b = 34 ft, and c = 42 ft.

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S = ½(a + b + c).