Question

an unusually shaped section of a park is to be paved. this section is drawn to scale below. the length of a single grid segment is 1 m.

Answer 1

Since the length of a single grid square is 1m, then its area is:

`A=1m*1m=1m^2\text{.}`

Now, to compute the area of the given section we will use the following diagram.

To compute the area of each triangle we will use the following formula for the area of a triangle:

`\begin{gathered} A=(bh)/(2), \\ \text{where b is the base of the triangle and h is its height.} \end{gathered}`

And to compute the area of the rectangle we will use the following formula:

`\begin{gathered} A=bh, \\ \text{where b is the base of the rectangle and h is its height.} \end{gathered}`

Therefore the area of triangle A is:

`A_A=(6m\cdot2m)/(2)=6m^2\text{.}`

The area of triangle B is:

`A_B=(4m\cdot2m)/(2)=4m^2\text{.}`

The area of triangle C is:

`A_C=(3m\cdot1m)/(2)=1.5m^2\text{.}`

The area of triangle D is:

`A_D=(5m\cdot1m)/(2)=2.5m^2\text{.}`

The area of rectangle E is:

`A_E=12m^2\text{.}`

Finally, the area of the given section is:

`\begin{gathered} A=A_A+A_B+A_C+A_D+A_E \\ =6m^2+4m^2+1.5m^2+2.5m^2+12m^2=26m^2\text{.} \end{gathered}`

Answer:

The area of a single grid square is:

`1m^2\text{.}`

The approximate area of the section that will be paved is:

`26m^2\text{.}`