Question

the perimeter of a rhombus is 40cm. if one of its diagonal is 12cm, find area of rhombus​

Answer 1

Answer:

96 cm²

Step-by-step explanation:

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Answer 2

Answer:

96 cm²

Step-by-step explanation:

Given, Perimeter of a rhombus = 40cm

And we know that Perimeter of rhombus = 4 x (side)

∴ Side = 40/4 = 10 cm

So, side of a rhombus = 10 cm

Now, we know that diagonals of a rhombus bisect each other at 90°.

And, half of each diagonal and one side consecutively forms a right angled triangle.

So, Pythagoras theorem:-

(Base)² + (Perpendicular)² = (Hypotenuse)²

Let another diagonal be x and we know that one diagonal is 12cm

So, (Half of one diagonal)² + (Half of another diagonal)² = (Side)²

= (12/2)² + (x/2²) = (10)²

= (6)² + (x/2)² = 100

= x²/4 = 100 - 36

= x²/4 = 64

= x² = 256

= x = √(256)

= x = √(16²)

= x = 16

So, Length of another diagonal = 16 cm

∴ Area of rhombus = 1/2 × (diagonal₁) × (diagonal₂) = 1/2 × 12 × 16 = 6 × 16 = 96 cm²

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