Question

each side of rhombus is 3root5 and its one diagonal is twice the other ,then find the area of the quadrilateral . this question is from Mensuration of class8
question no 29

Answer 1

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Answer 2

Answer:

• Area of rhombus = 36 cm²

Step-by-step explanation:

Given :

Each side of rhombus is 3√5 cm.

Let the length of one diagonal be x

Length of other diagonal = 2x

As We know:

Diagonals of a rhombus bisect each other at 90°.

Let's Suppose:

ABCD is a rhombus and AC and BD are the two diagonals of the rhombus which bisect each other at 90°.

By applying Pythagoras theorem,

• AB² = AO² + BO²
• (3√5)² = (2x/2)² + (x/2)²
• 45 = x² + x²/4
• 45 = (4x² + x²)/4
• 45 × 4 = 5x²
• x² = 180/5
• x = √36 = 6

Length of one diagonal = x = 6 cm

Length of other diagonal = 2x = 2 × 6 = 12 cm

Area of Rhombus = ½(product of its diagonals) sq. units

Hence,  

Area of rhombus = 36 cm²