Math 1 · Unit 11 · Lesson 3 · part 2 of 5
Perimeter: every side, then add
Perimeter is the distance all the way around a shape.
Perimeter: every side, then add
Perimeter is the distance all the way around a shape. On the grid, that is Lesson 1 again for every side, then add. Each corner of the shape is a vertex (the plural is vertices).
Start with a rectangle you can count: (1, 1), (6, 1), (6, 4), (1, 4). The sides are 5, 3, 5, and 3, so the perimeter is 16.
Now a pentagon with slanted sides: C(−1, 1), D(3, 4), E(6, 0), F(2, −3), G(−4, −4). Draw the right triangle under each side.
| side | from, to | legs | length |
|---|---|---|---|
| CD | (−1, 1) to (3, 4) | 4 and 3 | √4² + 3² = √25 = 5 |
| DE | (3, 4) to (6, 0) | 3 and 4 | √3² + 4² = √25 = 5 |
| EF | (6, 0) to (2, −3) | 4 and 3 | √4² + 3² = √25 = 5 |
| FG | (2, −3) to (−4, −4) | 6 and 1 | √6² + 1² = √37 ≈ 6.08 |
| GC | (−4, −4) to (−1, 1) | 3 and 5 | √3² + 5² = √34 ≈ 5.83 |
Three sides are exactly 5. The other two are √37 ≈ 6.08 and √34 ≈ 5.83. Add: 5 + 5 + 5 + 6.08 + 5.83 ≈ 26.91.