Question

1. Find the area of quadrilateral ABCD in which AB = 16cm, BC =CD = 26 cm, AD =12 cm and the diagonal BD = 20cm.​

Answer 1

Answer:

$\textbf{Area of quadrilateral ABCD=336}\:cm^2$

Step-by-step explanation:

$\text{Area of quadrilateral= Area of triangle ABD+ Area of triangle BCD}$

$\textbf{Area of triangle ABD:}$

a=16 cm, b=20 cm, c=12 cm

$s=\frac{a+b+c}{2}=\frac{16+20+12}{2}$

$\implies\:s=\frac{48}{2}=24\:cm$

$\text{Area of triangle ABD}$

$=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{24(24-16)(24-20)(24-12)}$

$=\sqrt{24(8)(4)(12)}$

$=\sqrt{3*8*8*4*3*4}$

$=3*8*4$

$=96\:cm^2$

$\textbf{Area of triangle ABD:}$

a=26 cm, b=26 cm, c=20 cm

$s=\frac{a+b+c}{2}=\frac{26+20+26}{2}$

$\implies\:s=\frac{72}{2}=36\:cm$

$\text{Area of triangle ABD}$

$=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{36(36-26)(36-26)(36-20)}$

$=\sqrt{36(10)(10)(16)}$

$=6*10*4$

$=240\:cm^2$

$\text{Area of quadrilateral ABCD= Area of triangle ABD+ Area of triangle BCD}$

$\text{Area of quadrilateral ABCD=96+240}$

$\therefore\:\textbf{Area of quadrilateral ABCD=336}\:cm^2$

Answer 2

Answer:

Area of Quadrilateral ABCD=Area of triangleABC+area of Triangle BDC

366cm^2