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Each side of a rhombus is 10 cm long and one of its diagonal measures 16 cm. The area of the rhombus is ____ $c m 2$ .

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Detailed Solution

Each side of a rhombus is 10 cm long and one of its diagonal measures 16 cm. The area of the rhombus is 96

c m 2

.
Let the length of the other diagonal = x.
As, diagonals of a rhombus bisects each other,

OA = A C ÷ 2 OA = 16 ÷ 2 OA=8 cm

O B = x 2

Now, using Pythagoras theorem in triangle AOB.

h y p o t e n u s e 2 = b a s e 2 + p e r p e n d i c u l a r 2

A B = O A 2 + O B 2

102 = x 2 2 + 82 x 2 4 = 100 − 64

Length of other diagonal = 12 cm.
Now area of rhombus is,

= 12 × Diagonal 1 × Diagonal 2

= 12 × AC × BD

= 12 × 16 × 12 = 96 cm 2

Area of the rhombus is

96 cm 2

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