Question

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

Answer 1

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.