Question

The sides of a quadrilateral, taken in order are 5, 12, 14 and 15 metres respectively, and the angle contained by the first two sides is a right angle. Find its area.

Answer 1

$\text{Let the sides of the quadrilareal be}$

$\text{u=5m, v=12m, x=14m and y=15m}$

$\text{Since the angle contained by a and b is right angle,}$

$u^2+v^2=\text{Hypotenuse}^2$

$25+144=\text{Hypotenuse}^2$

$169=\text{Hypotenuse}^2$

$\text{Hypotenuse}=13\;\text{m}$

$\textbf{Finding area of the triangle having sides 5m, 12m and 13m}$

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

$s=\dispalystyle\frac{5+12+13}{2}$

$s=15$

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

$\text{Area=}\sqrt{15(15-5)(15-12)(15-13)}$

$\text{Area=}\sqrt{15(10)(3)(2)}$

$\text{Area=}\sqrt{900}$

$\text{Area=}30\;\text{square meter}$

$\textbf{Finding area of the triangle having sides 13m, 14m and 15m}$

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

$s=\dispalystyle\frac{13+14+15}{2}$

$s=21$

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

$\text{Area=}\sqrt{21(21-13)(21-14)(21-15)}$

$\text{Area=}\sqrt{21(8)(7)(6)}$

$\text{Area=}\sqrt{(7)(16)(7)(9)}$

$\text{Area=}84\;\text{square meter}$

$\therefore\textbf{The area of the given quadrilateral}$

$\text{=30+84 square meter}$

$\text{=114 square meter}$