Math, asked by jaisingadi6050, 9 months ago

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.

Answers

Answered by MaheswariS
5

\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}

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