Question

5.) figure 12.16 shows the floorplan for a modern one story house. Bob calculates the area of the floor of the housing this way: 36•72-18•18 = 2268 feet squared. what might Bob have in mind? Explain why Bob’s method is a legitimate way to calculate the floor area of the house, and explain clearly have one or both of the moving and additivity principles on area apply in this case

Answer 1

From the given image, the Area of the floor can be calculated by removing/subtracting the area of the two triangles from the area of the rectangle.

Area of a rectangle is;

`\begin{gathered} A_r=lb \\ A_r=36.72 \end{gathered}`

Area of the two triangles;

`\begin{gathered} A_t=(1)/(2)bh+(1)/(2)bh=(1)/(2)(18.18)+(1)/(2)(18.18) \\ A_t=18.18 \end{gathered}`

The Area of the floor is;

`\begin{gathered} A=A_r-A_t \\ A=36.72-18.18 \\ A=2592-324 \\ A=2268ft^2 \end{gathered}`