Question

Find the perimeter of the shape below:

Answer 1

I see 3 right triangles.

Right triangle: a² + b² = c²
a = long leg ; b = short leg ; c = hypotenuse
hypotenuse = EH
a = 6 - 3 = 3
b = 3 - 1 = 2
c² = 3² + 2²
c² = 9 + 4
c² = 11
c = √11
c = 3.32

hypotenuse = FG
a = 3 ; b = 1
c² = 3² + 1²
c² = 9 + 1
c² = 10
c = √10
c = 3.16

hypotenuse = EF
a = 3 ; b = 2
c² = 3² + 2²
c² = 9 + 4
c² = 11
c = √11
c = 3.32

perimeter = 3.32 + 3.16 + 3.32 + 2 = 11.8 

Answer 2

The perimeter of the polygon to the nearest tenth of a unit $\boxed{12.4{\text{ units}}}$. Option (a) 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 $\left( { -1, 6} \right),\left( {2, 4} \right),\left( {- 1, 3} \right)$, and $\left( { - 3, 3} \right).$

Explanation:

The coordinates of the vertices of the polygon are $\left( { -1, 6} \right),\left( {2, 4} \right),\left( {- 1, 3} \right)$, and $\left( { - 3, 3} \right).$

The distance between point E and point F can be calculated as follows,

$\begin{aligned}{\text{Distance}}&= \sqrt {{{\left( { - 1 - 2} \right)}^2} + {{\left( {6 - 4} \right)}^2}}\\&= \sqrt {9 + 4}\\&= \sqrt {13}\\&= 3.6\\\end{aligned}$

The distance between points $\left( {2, 4} \right)$ and $\left( {- 1, 3} \right)$ can be calculated as follows,

$\begin{aligned}{\text{Distance}}&= \sqrt {{{\left( { - 1 - 2} \right)}^2} + {{\left( {3 - 4} \right)}^2}}\\&= \sqrt {9 + 1}\\&= \sqrt {10}\\&= 3.2\\\end{aligned}$

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

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

The distance between point $\left( { -1, 6} \right)$ and $\left( { - 3, 3} \right)$can be calculated as follows,

$\begin{aligned}{\text{Distance}} ^&= \sqrt {{{\left( { - 3 + 1} \right)}^2} + {{\left( {3 - 6} \right)}^2}}\\&= \sqrt {4 + 9}\\&= \sqrt {13}\\&= 3.6\\\end{aligned}$

The perimeter of the polygon can be calculated as follows,

$\begin{aligned}{\text{Perimeter}} &= 3.6 + 3.6 + 2 + 3.2\\&= 12.4\\\end{aligned}$

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 $\boxed{12.4{\text{ units}}}$. Option (a) 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.