Chapter 0.8, Problem 18E

To determine

To calculate: The area of the polygon provided below,

  

Answer to Problem 18E

The area of the polygon is $\text{31 square units}$ .

Explanation of Solution

Given information:

The figure is provided below,

  

Formula used:

Area of a polygon on square sheet is the number of full squares, half squares and almost-full squares that covers the surface of the figure.

Almost-full squares are counted as full squares.

Two half squares are equal to one whole square.

The squares which are less than half full are not counted.

Calculation:

Consider the provided figure,

  

Recall that area of a polygon on square sheet is the number of full squares, half squares and almost-full squares that covers the surface of the figure.

To evaluate the area of the polygon, we need to count the number of full squares, half squares and almost-full squares.

Number of full squares $=26$ .

Number of almost full squares $=4$ .

Recall almost-full squares are counted as full squares.

Number of half squares $=2$ .

And we know that two half squares are counted as one whole square.

So, $\frac{2}{2}=1$

There are 2 squares which are less than half full, so, they won’t be counted.

To estimate the area of the polygon, add the above number of squares.

  $\begin{array}{c}\text{A=26+4+1}\\ \text{=31}\end{array}$

Thus, the area of the polygon is $31$ square units.