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:

$A=1m\times1m=1m^2\text{.}$

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:

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

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:

$A_A=\frac{6m\cdot2m}{2}=6m^2\text{.}$

The area of triangle B is:

$A_B=\frac{4m\cdot2m}{2}=4m^2\text{.}$

The area of triangle C is:

$A_C=\frac{3m\cdot1m}{2}=1.5m^2\text{.}$

The area of triangle D is:

$A_D=\frac{5m\cdot1m}{2}=2.5m^2\text{.}$

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:

$26m^2\text{.}$