Question

Draw quadrilateral ABCD with the following measurements. Also find its area.
AB = 5 cm, BD = 7 cm, BC = 4 cm, $\angle$ BAD = ${100}^o$ and $\angle$ DBC = ${60}^o$ .

Answer 1

Area ABCD = ar $△$ABD + ar $△$BCD

ar $△$ABD = $\sqrt{s(s-a)(s-b)(s-c)},s=\frac{a+b+c}{2}=\frac{7+5+4.2}{2}=8.1cm$

= $\sqrt{8.1(8.1-7)(8.1-5)(8.1-4.2)}=\sqrt{8.1\times 1.1\times 3.1\times 3.9}$

= 10.40${cm}^2$

ar $△$BCD = $\sqrt{s(s-a)(s-b)(s-c)},s=\frac{7+6+4}{2}=8.5cm$

= $\sqrt{8.5(8.5-7)(8.5-6)(8.5-4)}=\sqrt{8.5\times 1.5\times 2.5\times 4.5}$

$\approx$ ${12cm}^2$

ar ABCD = 12 + 10.40 = 22.40