Question

The length of two adjacent sides of a parallelogram are $17$ cm and $12$ cm. one of its diagonals is $25$ cm long. Find the area of the parallelogram.

Answer 1

To find AE?

Area of $\Delta ABC=\sqrt{s(s-a)(s-b)(s-c)}$

here in $\Delta ABCa=25,b=17,c=15$

$s=\frac{25+17+12}{2}=\frac{54}{2}=27cm$

$\Delta ABC=\sqrt{27(27-25)(27-17)(27-12)}$

$=\sqrt{\mathrm{27.2.13.12}}$

$=\mathrm{3.3.2.}\sqrt{13}$

$=18\sqrt{13}c{m}^2$

Area of parallelogram $=2\times$ Area of $\Delta ABC$ $=18\times 2\sqrt{13}c{m}^2$

$=36\sqrt{13}c{m}^2$

$=129.8c{m}^2$

$\therefore$ Area of parallelogram $=129.8c{m}^2$.