Question

2 adjacent sides of a parallelogram are 28cm and 26cm. If 1 diagonal of it is 30cm long; find the area of parallelogram. Also find the distance between its shorter sides.

Answer 1

$\bold\green{\underline{Given:}}$

Two adjacent sides of parallelogram=28cm and 26cm

The 1 diagonal of parallelogram=30cm

$\bold\green{\underline{Find:Area\:and\: distance\: between\:its\: shorter\:sides}}$

$\bold\red{\underline{Solution:}}$

By using formula here

$\bold\purple{\boxed{Semi\: perimeter=\frac{a+b+c}{2}}}$

Here, a=28 b=26 c=30

⟹Semi perimeter=28+26+30/2

⟹Semi perimeter=84/2

⟹Semi perimeter=42cm

Now,

• Using heron's formula to calculate the area ∆

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

⟹Area=√s(s-a)(s-b)(s-c)

⟹Area=√42(42-28)(42-26)(42-30)

⟹Area=√42*14*16*12

⟹Area=√112896

⟹Area=336cm²

Now,

⟹Area of parallelogram=336*2

⟹Area of parallelogram=672cm²

Distance between its shorter sides=28-26=2cm