Question

$ PQRS$ is a parallelogram (Figure). $ QM$ is the height from $ Q$ to $ SR$ and $ QN$ is the height from $ Q$ to $ PS$. If $ SR=12 \mathrm{cm} \mathrm{and} QM=7.6 \mathrm{cm}$. Find:

(a) The area of the parallelogram $ PQRS$

(b) $ QN$ if $ PS=8 \mathrm{cm}$.

Answer 1

Step 1: Determine the area of parallelogram $PQRS$.

It is given that $SR=12\mathrm{cm}\mathrm{and}QM=7.6\mathrm{cm}$.

It is known that area of parallelogram is $A=b\times h$, where $b$ is the base and $h$ is the height.

Since $SR$ is the base and $QM$ is the height, the area is as follows:

$\begin{array}{rcl}A& =& 12\times 7.6\\ & \Rightarrow & A=91.2{\mathrm{cm}}^2\end{array}$

Hence, the area of a parallelogram $PQRS$ is $91.2{cm}^2$.

Step 2: Determine $QN$ if $PS=8\mathrm{cm}$.

The area of a parallelogram is $91.2{cm}^2$.

Since $PS$ is the base and $QN$ is the height, the area is as follows:

$\begin{array}{rcl}A& =& 8\times QN\\ & \Rightarrow & 91.2=8\times QN\\ & \Rightarrow & QN=\frac{91.2}{8}\\ & \Rightarrow & QN=11.4\mathrm{cm}\end{array}$

Hence, the value of $QN$ is $11.4\mathrm{cm}$.