Question

Find the area of the polygon ABCDE whose measurementrs in meter are given in the following figure.

Answer 1

$\to$ There are three triangles comprising the pentagon

& area of triangle by heron's formula = $\sqrt{s(s-a)(s-b)(s-c)}$

${△}_1$

a = b = 8 , c = 12

$S=\frac{8+8+12}{2}=14$

${△}_1=\sqrt{14\left(6\right)\left(6\right)\left(2\right)}$

$=6\times 2\sqrt{7}$

${△}_2$

a = b = 12, b = 10

S = 17

${△}_2\sqrt{17\left(5\right)\left(5\right)\left(7\right)}$

$=5\sqrt{119}$

${△}_3$

a = 10, b = 10, c = 12

S = 16

${△}_3=\sqrt{16\left(6\right)\left(6\right)\left(4\right)}$

$=6\times 4\times 2=48$

$\Rightarrow$ Total area $=48+12\sqrt{7}+5\sqrt{119}{m}^2$