Question

Use Heron's Formula, that is, the area of a triangle is A= s(s-a)(s-b)(s-c), where the(a+b+c) to find the area of the triangle with sidetriangle contains sides a, b and c andlengths: a = 6.2, b = 7.5, C = 4.9.18.4 square units23.3 square units15.1 square units28.5 square units

Answer 1

Heron's formula is given as

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

and

$s\text{ =}\frac{1}{2}(a+b+c)$

we are given that

$a=6.2,\text{ b = 7.5 and c = 4.9}$

First, we find the value of s using the formula

$\begin{gathered} s\text{ = }\frac{1}{2}(6.2\text{ + 7.5 + 4.9)} \\ s\text{ = }\frac{18.6}{2} \\ s\text{ = 9.3} \end{gathered}$

next, we substitute values of a, b, c, and s to get the area

$\begin{gathered} A\text{ = }\sqrt[]{s(s-a)(s-b)(s-c)} \\ A\text{ = }\sqrt[]{9.3(9.3-\text{ 6.2)(9.3 - 7.5)(9.3 - 4.9) }} \\ A\text{ = }\sqrt[]{9.3\text{ }\times3.1\times\text{ 1.8 }\times\text{ 4.4}} \\ A\text{ = }\sqrt[]{228.33} \\ A\text{ = 15.1 square units} \end{gathered}$

Therefore,

Area of triangle = 15.1 square units