**Question 5**:

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**:$\begin{array}{l}PV=VU=TS=SR=QP\\ \text{Givenperimeterofthewholediagram}=310\text{cm}\\ \\ PV+VU+UT+TS+SR+RQ+QP=310\\ PV+PV+50+PV+PV+50+PV=310\\ 5PV+100=310\\ \text{}5PV=210\\ \text{}PV=42\text{cm}\end{array}$

**Question 6**:

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**:$\begin{array}{l}\text{UsingPythagoras}\text{'}\text{theorem}\\ M{G}^{2}=M{F}^{2}+F{G}^{2}\\ \text{}={5}^{2}+{12}^{2}\\ \text{}=25+144\\ \text{}=169\\ MG=13\text{cm}\\ \\ \text{Perimeterofthecolouredregion}\\ =13+13+5+12+5+12\\ =60\text{cm}\end{array}$

**Question 7**:

Diagram below shows a trapezium

*BCDE*and a parallelogram

*ABEF.*

*ABC*and

*FED*are straight lines.

The area of

*ABEF*is 72 cm

^{2}.

Calculate the area, in cm

^{2}, of trapezium

*BCDE.*

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

**Question 8**:

In diagram below,

*ACEF*is a trapezium and

*BCDG*is a square.

Calculate the area, in cm

^{2}, of the coloured region

*.*

**Solution**:$\begin{array}{l}\text{Areaoftrapezium}ACEF\\ =\frac{1}{2}\times \left(8+15\right)\times 10\\ =115{\text{cm}}^{2}\\ \\ \text{Areaofsquare}BCDG\\ =4\times 4\\ =16{\text{cm}}^{2}\\ \\ \text{Areaoftrapezium}GDEF\\ =\frac{1}{2}\times \left(4+15\right)\times 6\\ =57{\text{cm}}^{2}\\ \\ \text{Areaofcolouredregion}\\ =115-16-57\\ =42{\text{cm}}^{2}\end{array}$