Question

area of rhombus is 360 meter square. its height is 16 m , Find the perimeter ??????

Answer 1

Hi,

• Perimeter of Rhombus = 4 x side 
• Area of a rhombus = ½ [ product of the diagonals] 
• Area = Base x Height

Some solved examples : 


1) The side of a rhombus is 18 cm . Find its perimeter.
Solution : 
Perimeter of Rhombus = 4 x side 
⇒ = 4 x 18 
⇒ = 72 cm 
∴ Perimeter of Rhombus = 72 cm.
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2) Find the area of a rhombus having each side equal to 13 cm and one of whose diagonal is 24 cm.
Solution : 
Let ABCD is a rhombus with diagonals AC and BD which intersect each other at O.
AC = 24 ⇒ AO = 12 

Let BO = x and AB = 13 cm (given) 
By Pythagorean theorem 
c 2 = a 2 + b 2 
13 2 = 12 2 + x 2 169 = 144 + x 2 
x 2 = 169 – 144 
x 2 = 25
x = 5 cm
BO = 5 cm
Diagonal BD = 2 x 5 = 10 cm.
Area = ½ x [ product of diagonals]
= ½ x 24 x 10 
Area = 120 sq.cm

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3) If the area of a rhombus is 24 sq.cm and one of its diagonal is 4 cm find the length of the other diagonal.

Solution : 
Area = ½ x d1 x d2 
24 = ½ x 4 x d2 
24 = 2 x d2 
d2 = 24/2 
d2 = 12 cm

Hope it helps.