Estimated Perimeter: about 31 units Estimated Area: 51 square units
Practice makes perfect
We want to estimate the perimeter and the area of the shaded figure. We can do these things one at a time.
Estimated Perimeter
We can recall that a perimeter is the distance around the outside of a two-dimensional figure. We can approximate the perimeter of our figure by estimating the sum of all of its side lengths. Let's start by considering the given diagram!
Notice that the sides of our figure consist of grid square lengths and diagonal lengths. We can recall that each grid square length is 1 unit and that we can estimate the diagonal length to be about 1.5 units. We can add this information to our diagram.
Now we can calculate the number of grid square lengths. Let's do it!
We found that there are 16 grid square lengths. Next, we can calculate the number of diagonal lengths.
We found that there are 10 diagonal lengths around the figure. Finally, we can calculate the length of the perimeter. We can do so using a table.
Number
Length
Total Length
Grid Square
16
1
16* 1 =16
Diagonal
10
1.5
10* 1.5=15
We found that 16 grid square lengths have the length of 16 units and that 10 diagonal lengths have the length of about 15 units. Now we can add 16 units and 15 units to find the length of the perimeter.
Perimeter
16+15=31
The figure has the perimeter of about 31 units.
Estimated Area
We want to estimate the area of the composite figure. We can do so by calculating the number of grid squares and half grid squares in our figure. We can start by calculating the number of squares!
We found that there are 46 squares with the area of 1 square unit. Next, we can calculate the number of half squares.
We found that there are 10 half squares with the area of 0.5 square unit. Finally, we can calculate the area of the figure. We can do so using a table.
Number
Area
Total Area
Grid Square
46
1
46* 1 =46
Grid Half Square
10
0.5
10* 0.5=5
We found that 46 grid squares have the area of 46 units and that 10 half grid squares have the area of 5 units. Now we can add 46 square units and 5 square units to find the area of our figure.
Area
46+5=51
The figure has the area of 51 square units.
