Question

The perimeter of a rhombus is 20 cm. Find the area of its one of the diagonal is 6cm. Use herons formula

Answer 1

Answer:

p=20cm

side=20/4

side=5cm

Answer 2

Given:

• The perimeter of a rhombus is 20 cm.

• one of the diagonal is 6cm.

To find out:

Find the area of given rhombus?

Solution:

Let ABCD be the rhombus of perimeter 20 cm and diagonal AC = 6 cm

We have

AB + BC + CD + DA = 20

⇒ 4 AB = 20 [ AB = BC = CD = DA ]

⇒ AB = 20/4

⇒ AB = 5 cm

In ∆ ABC, We have

2s = AB + BC + AC

⇒ 2s = 5 + 5 + 6

⇒2s = 16

⇒ s = 8 cm

Therefore,

∆1 = Area of ∆ ABC = √8 ( 8 - 5 ) ( 8 - 5 ) ( 8 - 6 )

= √8 × 3 × 3 × 2

= √144

= 12 cm²

Hence, area of rhombus ABCD = ( 2 × 12 ) cm² = 24 cm²