Question

two adjacent sides of a parallelogram measures 5cm and 3.5cm . one of its diagonal measures 6.5 cm . find the area of parallelogram.

Answer 1

from diagonal and two sides find the area of the triangle using Hero Formula 
then multiply this area by 2

Answer 2

Answer:

The area of the parallelogram is  $10\sqrt3cm^2$                              

Step-by-step explanation:

Given : Two adjacent sides of a parallelogram measures 5 cm and 3.5 cm. One of its diagonal measures 6.5 cm.

To find : The area of parallelogram?

Solution :

We know that, the diagonal of parallelogram divides the parallelogram into two triangle of equal area.

So, We find the area of the triangle whose sides are 5 cm, 3.5 cm and 6.5 cm.

Applying Heron's formula,

$s=\frac{a+b+c}{2}\\\\s=\frac{5+3.5+6.5}{2}\\\\s=\frac{15}{2}=7.5 cm$

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

Substitute the values in the formula,

$A=\sqrt{7.5(7.5-3.5)(7.5-6.5)(7.5-5)}$

$A=\sqrt{7.5(4)(1)(2.5)}$            

$A=\sqrt{75}$

$A=5\sqrt3cm^2$

The area of parallelogram = 2(Area of the triangle)            

$Area=2(5\sqrt3)cm^2$

$Area=10\sqrt3cm^2$

Therefore, The area of the parallelogram is  $10\sqrt3cm^2$