Question

Find two sides of a parallelogram are 10cm and 7cm one of its diagonal is 13cm find its atea

Answer 1

Area of a quadrilateral
$d {}^{2} \div 2$
so we apply values
$13 {}^{2} \div 2 \\ 169 \div 2 \\ 84.5 \: cm {}^{2}$

Answer 2

Answer:

$\text{Area of parallelogram is } 40\sqrt3cm^2$

Step-by-step explanation:

Given the two sides of parallelogram 10 cm and 7 cm and one of its diagonal is 13 cm.

we have to find the area of parallelogram.

In ΔABD, all sides are known we will find the area of triangle by herons formula.

$Semiperimeter=\frac{7+13+10}{2}=15$

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

$Area=\sqrt{15(15-7)(15-13)(15-10)}$

$Area=\sqrt{15\times 8\times 2\times 5}=20\sqrt3cm^2$

As the diagonal of parallelogram divides the parallelogram in two triangles of equal area.

Area of parallelogram=2(Area of triangle ABD)

$Area=2\times 20\sqrt3=40\sqrt3cm^2$

which is required area.