**Question 9**:

In diagram below,

*ADB*is a right-angled triangle and

*DBFE*is a square.

*C*is the midpoint of

*DB*and

*CH*=

*CD*.

Calculate the area, in cm

^{2}, of the coloured region

*.*

**Solution**:$\begin{array}{l}\text{Areaof}\u25b3\text{}ABC\\ =\frac{1}{2}\times 6\times 8\\ =24{\text{cm}}^{2}\\ \\ \text{Areaoftrapezium}BCHF\\ =\frac{1}{2}\times \left(12+6\right)\times 6\\ =54{\text{cm}}^{2}\\ \\ \text{Areaof}CDEFH\\ =\left(12\times 12\right)-54\\ =144-54\\ =90{\text{cm}}^{2}\\ \\ \text{Areaofcolouredregion}\\ =24+90\\ =114{\text{cm}}^{2}\end{array}$

**Question 10**:

Diagram below shows a rectangle

*ACDE*.

Calculate the area, in cm

^{2}, of the coloured region

*.*

**Solution**:$\begin{array}{l}\text{UsingPythagoras}\text{'}\text{theorem(ReferForm2Chapter6)}\\ F{E}^{2}=D{F}^{2}-D{E}^{2}\\ \text{}={13}^{2}-{12}^{2}\\ \text{}=169-144\\ \text{}=25\\ FE=\sqrt{25}=5\text{cm}\\ \\ AF=8-5=3\text{cm}\\ AB=12-8=4\text{cm}\\ \\ \text{Areaofrectangle}ACDE\\ =8\times 12\\ =96{\text{cm}}^{2}\\ \\ \text{Areaof}\u25b3\text{}ABF\\ =\frac{1}{2}\times 3\times 4\\ =6{\text{cm}}^{2}\\ \\ \text{Areaof}\u25b3\text{}DEF\\ =\frac{1}{2}\times 5\times 12\\ =30{\text{cm}}^{2}\\ \\ \text{Areaofcolouredregion}\\ =96-30-6\\ =60{\text{cm}}^{2}\end{array}$

**Question 11**:

Diagram below shows a sketch of parallelogram shaped garden,

*PQRS*that consists of flower beds and a playground.

Calculate the area, in m

^{2}, of the flower beds.

**Solution**:$\begin{array}{l}\text{Areaflowerbed}\\ =\left(12\times 14\right)-\left(\frac{1}{2}\times 12\times 7\right)\\ =168-42\\ =126{\text{m}}^{2}\end{array}$