Question

Use the composite figures below to mark each statement as true or false. Justify your choices.A.The area of figure A can be found by determining the sum of the area of the rectangle and the area of a semicircle.B. The area of figure b can be found by decomposing the figure into a square and parallelogram.C. Figure b has a total area of 29.75 M2.D.The area of figure a is 45.99 m2 more than the area of figure B.

Answer 1

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

`\begin{gathered} A=\pi r^2 \\ \text{Where r is the radius }=(4)/(2)=2\text{ m} \\ \Rightarrow A=3.14*2^2 \\ A=3.14*4 \\ A=12.56m^2 \end{gathered}`

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

`\begin{gathered} \text{Area of Composite figure }=(5*3.5)+(3.5*3.5) \\ =17.5+12.25 \\ =29.75m^2 \end{gathered}`

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