Question

Use Heron's formula to find the area of a triangle given side lengths a=6 meters, b=16 meters, and c=21 meters.

Answer 1

Answer:

30.31 m²

Step-by-step explanation:

Area of triangle using Heron's formula:

Find the semi perimeter S.

a = 6 m; b = 16 m; c =21 m

$\sf S = \dfrac{a + b + c}{2}\\\\\\S = \dfrac{6 +16 + 21}{2}\\\\\\S=\dfrac{43}{2}\\\\\\S = 21.5 \ m$

S - a = 21.5 - 6 = 15.5

S - b = 21.5 - 16 = 5.5

S - c = 21.5 - 21 = 0.5

Now, substitute all the values in the formula and find the area of the triangle.

$\boxed{\bf Area \ of \ triangle = \sqrt{S*(S - a) * (S-b) * (S-c)}}$

                                $\sf = \sqrt{21.5 * 15.5 * 5.5 * 0.5}$

                                $\sf = \sqrt{\dfrac{215 * 155 * 55 * 5}{10*10*10*10}}\\\\\\=\sqrt{\dfrac{5*43 * 5*31 * 5 * 11 * 5}{10*10*10*10}}\\\\\\=\dfrac{5*5}{10*10}\sqrt{43*31*11}\\\\\\= 0.25 * \sqrt{14694}\\\\=0.25 * 121.22\\\\= 30.31 \ m^2$