10.2.1 Perimeter and Area, PT3 Practice

Question 1:
In the diagram, ABCD is a trapezium and ABEF is a parallelogram.

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

Solution:
$\begin{array}{l}\text{Area of trapezium }ABCD\\ =\frac{1}{2}\times \left(8+14\right)\times 10\\ =110{\text{ cm}}^2\\ \\ \text{Area of parallelogram }ABEF\\ =8\times 6\\ =48{\text{ cm}}^2\\ \\ \text{Area of the shaded region}\\ =110-48\\ =62{\text{ cm}}^2\end{array}$

Question 2:
Diagram below shows a rectangle ABCD.


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

Solution:

$\begin{array}{l}\text{The area of the coloured region}\\ =\text{Area of rectangle}-\text{Area of trapezium}\\ =\left(12\times 8\right)-\frac{1}{2}\times \left(4+6\right)\times 4\\ =96-20\\ =76{\text{ cm}}^2\end{array}$

Question 3:
In diagram below, ACEF is a trapezium and BCDG is a square.


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

Solution:
$\begin{array}{l}\text{Area of trapezium }ACEF\\ =\frac{1}{2}\times \left(8+15\right)\times 10\\ =115{\text{ cm}}^2\\ \\ \text{Area of square }BCDG\\ =4\times 4\\ =16{\text{ cm}}^2\\ \\ \text{Area of trapezium }GDEF\\ =\frac{1}{2}\times \left(4+15\right)\times 6\\ =57{\text{ cm}}^2\\ \\ \text{Area of coloured region}\\ =115-16-57\\ =42{\text{ cm}}^2\end{array}$