Question

The sides of an isosceles triangle are 27, 27, and 12yd long. What is the area of the triangle?
Do not round any intermediate computations, and round your answer to the nearest tenth.

Answer 1

Solution

Using Heron's formula

$$S = \sqrt {p \times (p - a) \times (p - b) \times (p - c)},$$

where $a = 27$, $b = 27$, $c = 12$, $p = \frac{a + b + c}{2} = 33$.

$$S = \sqrt {33 \times (33 - 27) \times (33 - 27) \times (33 - 12)} = \sqrt {33 \times 6 \times 6 \times 21} = \sqrt {24948} = 157,9$$

Answer: the area of triangle is 157,9 yd.