Question

find the area and the perimeter of a rhombus in which diagonals are 6cm and 8cm​

Answer 1

Solution :-

Given - PQRS is a rhombus and we know that all four sides of a rhombus are of equal length.  

And, In Δ POQ  

PQ is hypotenuse, OP is base and OQ is perpendicular.

Using Pythagoras Theorem -

⇒ (PQ)² = (OP)² + (OQ)²

⇒ (PQ)² = (3)² + (4)²

⇒ (PQ)² = 9 + 16

⇒ (PQ)² = 25

⇒ PQ = √25

⇒ PQ = 5 cm

So, length of each side of the given rhombus is 5 cm.

Perimeter of rhombus = 4 × side  

⇒ 4 × 5

= 20 cm

So, perimeter of the rhombus PQRS is 20 cm.

Answer 2

Answer:

Area = 24cm²

Perimeter = 20 cm

Step-by-step explanation:

For finding area of the rhombus : Formula is

Area = ( diagonal 1 × diagonal 2) ÷2

By putting values , Area = ( 6× 8)÷2

=> 24 cm²

and for finding area , first we have find one side :

In Rhombus diagonals bisect each other at right angle

i.e, 6÷2= 3 and 8 ÷ 2 = 4

We got these value and by hypotenuse therom we can find the third value for side that is

s = root ( 3²+4⁴)

and s= 5

Perimeter = 4×s = 4×5= 20 cm