Question

The diagonal of rectangle ABCD is 5 cm. Find the area of parallelogram ABDE.

Answer 1

$\text{BC = AD = 5cm (side of rectangle)}$

$\text{in}\Delta \text{ABD}$

$\text{B}{\text{D}}^{\text{2}}=\text{A}{\text{D}}^{\text{2}}+\text{A}{\text{B}}^{\text{2}}$

${13}^2=5^2+\text{A}{\text{B}}^{\text{2}}$

$\text{A}{\text{B}}^{\text{2}}={13}^2-5^2$

$\text{A}{\text{B}}^{\text{2}}={169}^2-25$

$\text{A}{\text{B}}^{\text{2}}=144$

$\text{AB = 12cm}$

$\text{area of Parllangle ABDE}$

$\text{=}\frac{1}{2}\times \text{AD}\times \text{AB}$

$=\frac{1}{2}\times 5\times 12$

$=30cm$