Question

In Fig. 12.8, PQRS is a parallelogram, HSR isa straight line and HPQ = 90°. If|HQ| = 10 cm and |PQ| = 6 cm, what is thearea of the parallelogram?

Answer 1

48 cm²

Explanation

First, we need to calculate the height of the parallelogram, segment HP. Applying the Pythagorean theorem to triangle HPQ, we get:

`\begin{gathered} HQ^2=HP^2+PQ^2 \\ \text{ Substituting with HQ = 10 cm, and PQ = 6 cm, and solving for HP:} \\ 10^2=HP^2+6^2 \\ 100=HP^2+36 \\ 100-36=HP^2 \\ 64=HP^2 \\ √(64)=HP \\ HP=8\text{ cm} \end{gathered}`

The area of a parallelogram is calculated as follows:

`A=base* height`

In this case, the height is HP = 8 cm, and the base is PQ = 6 cm. Then the area of parallelogram PQRS is:

`\begin{gathered} A=HP* PQ \\ A=8*6 \\ A=48\text{ cm}^2 \end{gathered}`