Question

Find the area of a rhombus whose side 8cm and whose altitude is 0.5 dm.

Answer 1

The answer is 31.2 cm²

GIVEN

Side of the rhombus = 8cm

Length of the altitude = 0.5 dm

TO FIND

Area of the rhombus.

SOLUTION

The above problem can be simply solved as follows;

Let the rhombus be ABCD

Let the diagonals intersect at 'O' .

It is known that the diagonals bisect eachother their point of intersection.

D₁ = AC

D₂ = BD

Applying pythagour theorem in ΔABO

AB² = AO² + BO²

8² = 5² + BO²

64 = 25 + BO²

BO² = 64 - 25

= 39

BO = √39

= 6.24 cm

Length of the diagonal = 2 × BO = 6.24 × 2 = 12.48

Formula to calculate area of the rhombus = (d₁ × d₂) ÷ 2

= (5 × 12.48) ÷ 2

= 62.4 ÷ 2

= 31.2cm²

Hence, The answer is 31.2 cm²

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