Resources for Perimeter, Area and Volume
-
Questions
7
With Worked SolutionClick Here -
Video Tutorials
3
Click Here -
HSC Questions
2
With Worked SolutionClick Here
Perimeter, Area and Volume Theory
![Perimeter of a shape can be determined by determining the distance around the diagram and multiplying by the scale to determine the actual perimeter.\\ The area of a shape can be determined by using the trapezoidal rule\\ \(A=\dfrac{w}{2}\left(d_f+d_l\right)\)\\ where \\ \(w=\) width between parallel sides \\ \(d_f=\) distance along first parallel side \\ \(d_l=\) distance along the last parallel side\\ The volume of a shape can be determined by the formula\\ \(V=A h\)\\ where \\ \(A=\) area of the cross -section of the prism.\\ \(h=\) height.\\ \begin{multicols}{2} \textbf{Example 1}\\ A diagram has a scale of \(1: 50\). What is the actual perimeter of a circle with a radius of \(12 \mathrm{~mm}\)?\\ \textbf{Example 1 solution}\\ $\begin{aligned} C &=2 \pi r \\ &=2 \pi \times 12 \\ \text { Actual permeter } & =2 \pi \times 12 \times 50 \\ & =3770 \mathrm{~mm} \\ & =3.77 \mathrm{~m} \end{aligned}$\\ \textbf{Example 2}\\ Using the trapezoidal rule, the area of the following figure is? \\ \begin{center} \includesvg[width=0.4\textwidth]{91a8e1f3-38b6-480f-b55b-09ae1d0eec0b} \end{center} \columnbreak \textbf{Example 2 solution}\\ $\begin{aligned}\text { Area }=\frac{w}{2}(&\left.d_{f}+d_{l}\right) \\\text { Total Area } &=\frac{60}{2}(0+10)+\frac{60}{2}(10+8) \\&=840 \mathrm{~m}^{2}\end{aligned}$\\ \textbf{Example 3}\\ A diagram has a scale 1:100. What is the actual volume of a cube with side \(4 \mathrm{~cm}\) ?\\ \textbf{Example 3 solution}\\ $\begin{aligned} \text { Actual length } & =4 \times 100 \\ & =400 \mathrm{~cm} \\ & =4 \mathrm{~m} \\ \text { Volume } & =4 \times 4 \times 4 \\ & =64 \mathrm{~m}^3 \end{aligned}$\\ \end{multicols}](/media/wokp0ghw/4315.png)