Question

Find the area of the triangle below.Carry your intermediate computations to at least four decimal places. Round your answer to the nearest tenth.14 km10 km| km?х15 km

Answer 1

Since all the sides of the triangle are known, it is better to use Heron's formula for finding the area.

Consider the sides of the triangle as,

`\begin{gathered} a=10 \\ b=14 \\ c=15 \end{gathered}`

Solve for the semi-perimeter (s) as,

`\begin{gathered} s=(a+b+c)/(2) \\ s=(10+14+15)/(2) \\ s=19.5 \end{gathered}`

Then according to the Heron's Formula, the area (A) of the triangle is given by,

`A=\sqrt[]{s(s-a)(s-b)(s-c)}`

Substitute the values and simplify,

`\begin{gathered} A=\sqrt[]{19.5(19.5-10)(19.5-14)(19.5-15)} \\ A=\sqrt[]{19.5*9.5*5.5*4.5} \\ A=\sqrt[]{4584.9375} \\ A\approx67.7 \end{gathered}`

Thus, the area of the given triangle is 67.7 sq. km approximately.