Question

Find the perimeter of the shape below:

Answer 1

The perimeter of the polygon to the nearest tenth of a unit $\boxed{13.6{\text{ units}}}$. Option (d) is correct.

Further explanation:

The distance between the two points can be calculated as follows,

$\boxed{{\text{Distance}} = \sqrt {{{\left( {{x_2} - {x_1}} \right)}^2} + {{\left( {{y_2} - {y_1}} \right)}^2}} }$

Given:

The coordinates of the vertices of the polygon are $\left( { -2, 7} \right),\left( {2, 5} \right),\left( {- 1, 5} \right)$, and $\left( { - 1, 3} \right).$

Explanation:

The coordinates of the vertices of the polygon are $\left( { -2, 7} \right),\left( {2, 5} \right),\left( {- 1, 5} \right)$, and $\left( { - 1, 3} \right).$

The distance between points $\left( { -2, 7} \right)$ and $\left( {2, 5} \right),$ can be calculated as follows,

$\begin{aligned}{\text{Distance}} &= \sqrt {{{\left( { - 2 - 2} \right)}^2} + {{\left( {5 - 7} \right)}^2}}\\&= \sqrt {16 + 4}\\&= \sqrt {20}\\&= 4.47\\\end{aligned}$

The distance between points $\left( {2, 5} \right)$ and $\left( {- 1, 5} \right)$ can be calculated as follows,

$\begin{aligned}{\text{Distance}}&= \sqrt {{{\left( { - 1 - 2} \right)}^2} + {{\left( {5 - 5} \right)}^2}}\\&= \sqrt {9 + 0}\\&= \sqrt9\\&= 3\\\end{aligned}$

The distance between points $\left( {- 1, 5} \right)$, and $\left( { - 1, 3} \right)$ can be calculated as follows,

$\begin{aligned}{\text{Distance}} &= \sqrt {{{\left( { - 1 + 1} \right)}^2} + {{\left( {3 - 5} \right)}^2}}\\&= \sqrt {0 + 4}\\&= \sqrt4\\&= 2\\\end{aligned}$

The distance between point $\left( { -2, 7} \right)$ and $\left( { - 1, 3} \right)$ can be calculated as follows,

$\begin{aligned}{\text{Distance}} &= \sqrt {{{\left( { - 1 + 2} \right)}^2} + {{\left( {3 - 7} \right)}^2}} \\&= \sqrt {1 + 16} \\&= \sqrt {17} \\&= 4.13\\\end{aligned}$

The perimeter of the polygon can be calculated as follows,

$\begin{aligned}{\text{Perimeter}} &= 4.47 + 3 + 2 + 4.13\\&= 13.6\\\end{aligned}$

Option (a) is not correct.

Option (b) is not correct.

Option (c) is not correct.

The perimeter of the polygon to the nearest tenth of a unit $\boxed{13.6{\text{ units}}}.$ Option (d) is correct.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Coordinate geometry

Keywords: perimeter, shape, perimeter of shape below, Coordinates, vertices, polygon, x-coordinate, y-coordinate, perimeter, circumference, nearest tenth unit, distance formula.

Answer 2

The perimeter is the sum of the length of the line segments.
Length of RS = sqrt((-2 - (-1))^2 + (7 - 3)^2) = sqrt((-1)^2 + 4^2) =sqrt(1 + 16) = sqrt(17) = 4.12 units
Length of ST = sqrt((2 - (-2))^2 + (5 - 7)^2) = sqrt(4^2 + (-2)^2) = sqrt(16 + 4) = sqrt(20) = 4.47 units
Length of TU = 3 units
Length of UR = 2 units

Perimeter = 4.12 + 4.47 + 3 + 2 = 13.6 units.