To find the perimeter of the polygon with vertices at \((1, 3)\), \((7, 3)\), \((7, 7)\), and \((4, 7)\), we need to calculate the lengths of each of its sides and then add them together.
1. Calculate the distance between \((1, 3)\) and \((7, 3)\):
\[
\text{Distance} = \sqrt{(7 - 1)^2 + (3 - 3)^2} = \sqrt{6^2 + 0^2} = 6
\]
2. Calculate the distance between \((7, 3)\) and \((7, 7)\):
\[
\text{Distance} = \sqrt{(7 - 7)^2 + (7 - 3)^2} = \sqrt{0^2 + 4^2} = 4
\]
3. Calculate the distance between \((7, 7)\) and \((4, 7)\):
\[
\text{Distance} = \sqrt{(4 - 7)^2 + (7 - 7)^2} = \sqrt{(-3)^2 + 0^2} = 3
\]
4. Calculate the distance between \((4, 7)\) and \((1, 3)\):
\[
\text{Distance} = \sqrt{(1 - 4)^2 + (3 - 7)^2} = \sqrt{(-3)^2 + (-4)^2} = \sqrt{9 + 16} = 5
\]
Now sum all the side lengths:
\[
6 + 4 + 3 + 5 = 18
\]
Therefore, the perimeter of the polygon is \(\boxed{18}\) units.
13.
Find the perimeter of the polygon with vertices at (1, 3), (7, 3), (7, 7), and (4, 7).
13 units
18 units
22 units
20 units
1 answer