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14

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

Length of side of rhombus = 20 cm

Length of one diagonal = 24 cm

In ΔAOB

Using pythagorous theorem:

AB^{2} = OA^{2} + OB^{2}

20^{2} - 12^{2} = OB^{2}

OB^{2} = 400 – 144

OB^{2} = 256

OB = 16

Hence, length of other diameter = 16 × 2 = 32 cm

Area of rhombus =

Area of rhombus =

Area of rhombus = 384 cm^{2}