Question

Find the area of a quadrilateral ABCD in which AB = 42cm, BC = 21cm, CD = 29 cm, DA = 34 cm and diagonal BD = 20 cm.

Answer 1

In quadrilateral ABCD,
AB = 42 cm, BC = 21 cm, CD = 29 cm
DA = 34 cm, BD = 20 cm

Area of $\Delta ABD,s=\frac{a+b+c}{2}\Rightarrow s=\frac{42+20+34}{2}=\frac{96}{2}=48\therefore Area=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{48(48-42)(48-20)(48-34)}=\sqrt{48\times 6\times 28\times 14}=\sqrt{4\times 4\times 3\times 3\times 2\times 2\times 14\times 14}=4\times 3\times 2\times 14=336c{m}^2$
Area of $\Delta BCD,$
$\therefore s=\frac{a+b+c}{2}s=\frac{20+21+29}{2}=\frac{70}{2}=35\therefore Area=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{35(35-20)(35-21)(35-29)}=\sqrt{35\times 15\times 14\times 6}=\sqrt{7\times 5\times 5\times 3\times 3\times 2\times 2\times 7}=7\times 5\times 3\times 2=210c{m}^2$
$\therefore$ Area of quadrilateral ABCD,
= $336+210=546c{m}^2$