Question

a parallelogram has sides 13m and 14m and one of its diagonal is 20m long, so find the area of parallelogram.

use Heron's Formula​

Answer 1

Answer:

the area is 42819

Step-by-step explanation:

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Answer 2

To find : Area of parallelogram  

Given : sides of parallelogram are $13\ m$ and $14\ m$ .

            Diagonal = $20\ m$

Solution :

• Let ABCD be the given parallelogram.

• Area of parallelogram ABCD = $2 ( area \ of \ triangle\ ABC)$

• Now , a = $13\ m$ , b = $14\ m$

               $s = \frac{a + b +c }{2} \\s = \frac{13 + 14+ 20}{2} \\s = 23.5$

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

                                             $= \sqrt{23.5 ( 23.5 - 13 ) (23.5 - 14 ) (23.5 - 20 )} \\=\sqrt{23.5 ( 10.5 ) ( 9.5) ( 3.5 ) } \\= \sqrt{8204.4375} \\= 90.5783\ m^{2}$

• Area of parallelogram ABCD $= 2 \times 90.5783 \ m^{2}$

                                                         $= 181.1567 m^{2}$

Hence , area of parallelogram is $181.1567 m^{2}$ .