10.2.4 Perimeter and Area, PT3 Practice

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 cm², of the coloured region.

Solution:
$\begin{array}{l}\text{Area of }△ABC\\ =\frac{1}{2}\times 6\times 8\\ =24{\text{ cm}}^2\\ \\ \text{Area of trapezium }BCHF\\ =\frac{1}{2}\times \left(12+6\right)\times 6\\ =54{\text{ cm}}^2\\ \\ \text{Area of }CDEFH\\ =\left(12\times 12\right)-54\\ =144-54\\ =90{\text{ cm}}^2\\ \\ \text{Area of coloured region}\\ =24+90\\ =114{\text{ cm}}^2\end{array}$

Question 10:
Diagram below shows a rectangle ACDE.

Calculate the area, in cm², of the coloured region.

Solution:
$\begin{array}{l}\text{Using Pythagoras}‘\text{ theorem (Refer Form 1 Chapter 13)}\\ F{E}^2=D{F}^2-D{E}^2\\ ={13}^2-{12}^2\\ =169-144\\ =25\\ FE=\sqrt{25}=5\text{ cm}\\ \\ AF=8-5=3\text{ cm}\\ AB=12-8=4\text{ cm}\\ \\ \text{Area of rectangle }ACDE\\ =8\times 12\\ =96{\text{ cm}}^2\\ \\ \text{Area of }△ABF\\ =\frac{1}{2}\times 3\times 4\\ =6{\text{ cm}}^2\\ \\ \text{Area of }△DEF\\ =\frac{1}{2}\times 5\times 12\\ =30{\text{ cm}}^2\\ \\ \text{Area of coloured region}\\ =96-30-6\\ =60{\text{ cm}}^2\end{array}$

Question 11:
Diagram below shows a sketch of parallelogram shaped garden, PQRS that consists of flower beds and a playground.

Calculate the area, in m², of the flower beds.

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