Question

18. The sides of a parallelogram are 12 m and 17 m respectively. If one of
its diagonal measure 6.5 cm. Find the area of the parallelogram.​

Answer 1

Heya !

Given:-

• Side 1 of a parallelogram = 12 cm.
• Side 2 of a parallelogram = 17 cm.
• Diagonal of a parallelogram = 6.5 cm.

To find:-

• Area of the parallelogram

Knowledge required:-

• The diagonal of a parallelogram divides it into two triangles of equal area.
• So, we can find the area of 1 triangle by Heron's formula and multiply it with 2 to get the area of the parallelogram.

Formula required :-

$\huge \fbox \blue{Ar(∆) = √s(s-a)(s-b)(s-c)}$

$\implies$ S = 12+17+6.5/2

$\implies$ S = 35.5/2 = 17.75

Ar(∆) = √17.75(17.75-12)(17.75-17)(17.75-6.5)

$\implies$ √17.75(5.75)(0.75)(11.25)

$\implies$ √861.15 = 29.34 cm²

Area of the entire parallelogram = 2×29.34 = 58.68 cm²