Question

# Find the area of the rhombus one side of which measures 20cm and one of whose diagonals is 24cm.

Solution

## The diagonals of a rhombus bisect at right anglesConsider $$\Delta$$ AODUsing the Pythagoras theorem$$AD^2 = OD^2 + AO^2$$By substituting the values$$20^2 =OD^2 + 12^2$$On further calculation$$OD^2 = 400 - 144$$By subtraction$$OD^2 = 256$$By taking out the square rootOD = $$\sqrt{256}$$So we getOD = 16cmWe know that BD = 2ODSo we getBC = 2 (16) = 32cmWe know thatArea of rhombus ABCD = $$\dfrac{1}{2} \times AC \times BD$$By substituting the valuesArea of rhombus ABCD = $$\dfrac{1}{2} \times 24 \times 32$$On further calculationArea of rhombus ABCD = $$384 cm^2$$Therefore, the area of rhombus ABCD is $$384 cm^2.$$MathematicsRS AgarwalStandard IX

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