Answer
A. True
In figure A, there are two semicircles and a rectangle.
Area of the composite figure = Area of a circle + area of a rectangle
Two semicircles give a complete circle, therefore the area of a circle is given by
[tex]\begin{gathered} A=\pi r^2 \\ \text{Where r is the radius }=\frac{4}{2}=2\text{ m} \\ \Rightarrow A=3.14\times2^2 \\ A=3.14\times4 \\ A=12.56m^2 \end{gathered}[/tex]
The area of the rectangle in figure A is given by
A = length x width
A = 7 x 4
A = 28 m²
Therefore, the area of the composite figures = 12.56 m² + 28 m² = 40.56 m²
B. True
Note: label the figure from A - G and join line D to C as shown below.
Area of the composite figure = Area of parallelogram ABCE + Area of square CDFG
Note: Area of parallelogram = base x height
Area of a square = length x length
[tex]\begin{gathered} \text{Area of Composite figure }=(5\times3.5)+(3.5\times3.5) \\ =17.5+12.25 \\ =29.75m^2 \end{gathered}[/tex]
C. True
D. False, area of figure A is 40.56 m², and area of figure B is 29.75 m². Therefore, the area of figure A is 10.81 m² NOT 45.99 m². more than the area of figure B
