Question

Question 1 2. Find the area of the composite figure 10 ft 3 ft a) 40 b) 9 c) 49 d) 61 Your answer:

Answer 1

To obtain the area of the composite figure, the following steps are necessary:

Step 1: Separate the composite figure into its components and label as appropriate, as below:

Step 2: Find the area of the recatngle and right triangle as follows:

$\begin{gathered} \text{Area of rectangle= length }\times\text{ breadth} \\ \Rightarrow\text{Area of rectangle= }10ft\times4ft=40ft^2 \end{gathered}$

Also:

$\begin{gathered} \text{Area of triangle =}\frac{1}{2}\times base\times perpendicular\text{ height} \\ \Rightarrow\text{Area of triangle =}\frac{1}{2}\times6ft\times(4+3)ft \\ \Rightarrow\text{Area of triangle =}\frac{1}{2}\times6ft\times7ft=\frac{42}{2}ft^2=21ft^2 \\ \Rightarrow\text{Area of triangle =}21ft^2 \end{gathered}$

Step 3: Add the areas of the components to obtain the area of the composite figure, as follows:

$\begin{gathered} \text{Area of composite figure= area of triangle + area of rectangle} \\ \Rightarrow Areaofcompositefigure=21ft^2\text{ + }40ft^2 \\ \Rightarrow\text{Area of composite figure= 6}1ft^2 \end{gathered}$

Therefore, the area of the composite figure is 61 square feet (Option D)