Question

find the area of a rhombus whose one side is 20 cm and one diagonal is of 24 cm

Answer 1

Consider a rhombus ABCD with side length 20cm and diagonal BD = 24cm
BP = BD/2 =24/2= 12cm
Now triangle ABP
$({ AP })^{2} = ({AB})^{2} - ({BP})^{2} \: \: \: \: \: \: \: (by \: pythagoras \: \: theorem)\\ ({ AP })^{2} = (20)^{2} - (12) ^{2} \\({ A P })^{2} = 400 - 144 \\ ({ AP })^{2} = 256 \\ AP = 16cm \\ AC = 2AP = 2 \times 16 = 32cm \\ Area \: of \: rhombus = \frac{1}{2 } \times d1 \times d2 \\ = \frac{1}{2} \times 24 \times 32 \\ = 384 \: cm^{2}$