10.2.2 Perimeter and Area, PT3 Practice

Question 4:
In diagram below, PQUV is a square, QRTU is a rectangle and RST is an equilateral triangle.


The perimeter of the whole diagram is 310 cm.
Calculate the length, in cm, of PV.

Solution:
$\begin{array}{l}PV=VU=TS=SR=QP\\ \text{Given perimeter of the whole diagram}=310\text{ cm}\\ \\ PV+VU+UT+TS+SR+RQ+QP=310\\ PV+PV+50+PV+PV+50+PV=310\\ 5PV+100=310\\ 5PV=210\\ PV=42\text{ cm}\end{array}$

Question 5:
In diagram below, ABCD and CGFE are rectangles. M, G, E and N are midpoints of AB, BC, CD and DA respectively.


Calculate the perimeter, in cm, of the coloured region.

Solution:


$\begin{array}{l}\text{Using Pythagoras}‘\text{ theorem}\\ M{G}^2=M{F}^2+F{G}^2\\ =5^2+{12}^2\\ =25+144\\ =169\\ MG=13\text{ cm}\\ \\ \text{Perimeter of the coloured region}\\ =13+13+5+12+5+12\\ =60\text{ cm}\end{array}$

Question 6:
Diagram below shows a trapezium BCDE and a parallelogram ABEF. ABC and FED are straight lines.

The area of ABEF is 72 cm².
Calculate the area, in cm², of trapezium BCDE.

Solution:
$\begin{array}{l}\text{Base }\times \text{ Height }=\text{Area of }ABFE\\ 9\text{ cm }\times \text{ Height}=72{\text{ cm}}^2\\ \text{ Height}=\frac{72}{9}\\ =8\text{ cm}\\ CD=8\text{ cm}\\ BC=23-9\\ =14\text{ cm}\\ \\ \text{Area of trapezium }BCDE\\ =\frac{1}{2}\times \left(BC+ED\right)\times CD\\ =\frac{1}{2}\times \left(14+9\right)\times 8\\ =92{\text{ cm}}^2\end{array}$