Question

two adjacent sides of a parallelogram method 5 cm and 3.5 CM one of its diagonal measure 6.5 cm find the area of parallelogram

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Answer 1

Answer:

$\text{Area of parallelogram is }=10\sqrt3cm^2$

Step-by-step explanation:

Given two adjacent sides of parallelogram 5 cm and 3.5cm and one of its diagonal measure 6.5 cm. we have to find the area of parallelogram.

As the diagonal of parallelogram divides the parallelogram into two triangle of equal area. ∴ we find the area of triangle whose three sides are 5cm, 3.5cm and 6.5 cm.

By Heron's formula,

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

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

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

           =$\sqrt{7.5(4)(1)(2.5)}$

           =$\sqrt{75}=5\sqrt3cm^2$

hence, $\text{area of parallelogram is }=2\times5\sqrt3=10\sqrt3cm^2$

Answer 2

Answer:

Given, ABCD is a parallelogram having AB=5 cm,BC=3.5 cm and one of the diagonal AC=6.5 cm.

We know that the diagonal of a parallelogram divides it into two triangles of equal area.

Therefore, in triangle ABC, by heron's formula, we have a=5 cm,b=3.5 cm and c=6.5 cm

⇒ semi-perimeter of triangle ABC,s=

a+b+c = 5+3.5+6.5 =7.5 cm

  2                 2

∴ Area of triangle ABC=  

s(s−a)(s−b)(s−c)

=  7.5(7.5−5)(7.5−3.5)(7.5−6.5)

​=5  3 cm  

2

 

⇒ Area of parallelogram ABCD=2×area of triangle ABC=2×5  

3

​  

 cm  

2

=10  

3

​  

 cm  

2