Question

find the area of the triangle.
a 7
b 14
c 8

Explanation:

Step1: Calculate semi-perimeter

First, find the semi-perimeter $s$ of the triangle using the formula $s=\frac{a+b+c}{2}$.

$$ s=\frac{7+14+8}{2}=\frac{29}{2}=14.5 $$

Step2: Apply Heron's formula

Use Heron's formula $Area=\sqrt{s(s-a)(s-b)(s-c)}$ to compute the area.

$$ Area=\sqrt{14.5\times(14.5-7)\times(14.5-14)\times(14.5-8)} $$

$$ =\sqrt{14.5\times7.5\times0.5\times6.5} $$

$$ =\sqrt{\frac{29}{2}\times\frac{15}{2}\times\frac{1}{2}\times\frac{13}{2}} $$

$$ =\sqrt{\frac{29\times15\times1\times13}{16}}=\frac{\sqrt{29\times195}}{4}=\frac{\sqrt{5655}}{4}\approx\frac{75.2}{4}=18.8 $$

Answer:

$\frac{\sqrt{5655}}{4}$ or approximately $18.8$ square units