3. Perimeters and Areas of Composite Figures
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The grid square has a side length of 1 unit.
Estimated Perimeter: about 20 units
Estimated Area: 24 square units
We want to estimate the perimeter and the area of the shaded figure. We can do these things one at a time.
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.
We found that there are 8 grid square lengths. Next, we can calculate the number of diagonal lengths.
We found that there are 8 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 | 8 | 1 | 8* 1 =8 |
| Diagonal | 8 | 1.5 | 8* 1.5=12 |
We found that 8 grid square lengths have the length of 8 units and that 8 diagonal lengths have the length of about 12 units. Now we can add 8 units and 12 units to find the length of the perimeter. Perimeter 8+12=20 The figure has the perimeter of about 20 units.
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 20 squares with the area of 1 square unit. Next, we can calculate the number of half squares.
We found that there are 8 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 | 20 | 1 | 20* 1 =20 |
| Grid Half Square | 8 | 0.5 | 8* 0.5=4 |
We found that 20 grid squares have the area of 20 units and that 8 half grid squares have the area of 4 units. Now we can add 8 square units and 4 square units to find the area of our figure. Area 20+4=24 The figure has the area of 24 square units.