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labwork [276]
3 years ago
9

The coordinates of the vertices of a polygon are (-2, 1). (-3, 3), (-1, 5), (2, 4), and (2, 1). What is the perimeter of the pol

ygon to the nearest tenth of a unit.
Do not label your answer. Answer with a number only.

Mathematics
1 answer:
kobusy [5.1K]3 years ago
6 0

Answer:

15.2\ units

Step-by-step explanation:

step 1

Plot the vertices of the polygon to better understand the problem

we have

A(-2, 1). B(-3, 3), C(-1, 5), D(2, 4),E(2, 1)

using a graphing tool

The polygon is a pentagon (the number of sides is 5)

see the attached figure

The perimeter is equal to

P=AB+BC+CD+DE+AE

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

step 2

<em>Find the distance AB</em>

A(-2, 1). B(-3, 3)

substitute in the formula

d=\sqrt{(3-1)^{2}+(-3+2)^{2}}

d=\sqrt{(2)^{2}+(-1)^{2}}

d_A_B=\sqrt{5}=2.24\ units

step 3

<em>Find the distance BC</em>

B(-3, 3), C(-1, 5)

substitute in the formula

d=\sqrt{(5-3)^{2}+(-1+3)^{2}}

d=\sqrt{(2)^{2}+(2)^{2}}

d_B_C=\sqrt{8}=2.83\ units

step 4

<em>Find the distance CD</em>

C(-1, 5), D(2, 4)

substitute in the formula

d=\sqrt{(4-5)^{2}+(2+1)^{2}}

d=\sqrt{(-1)^{2}+(3)^{2}}

d_C_D=\sqrt{10}=3.16\ units

step 5

<em>Find the distance DE</em>

D(2, 4),E(2, 1)

substitute in the formula

d=\sqrt{(1-4)^{2}+(2-2)^{2}}

d=\sqrt{(-3)^{2}+(0)^{2}}

d_D_E=\sqrt{9}\ units

d_D_E=3\ units

step 6

<em>Find the distance AE</em>

A(-2, 1).E(2, 1)

substitute in the formula

d=\sqrt{(1-1)^{2}+(2+2)^{2}}

d=\sqrt{(0)^{2}+(4)^{2}}

d_A_E=\sqrt{16}\ units

d_A_E=4\ units

step 7

Find the perimeter

P=AB+BC+CD+DE+AE

substitute the values

P=2.24+2.83+3.16+3+4=15.23\ units

Round to the nearest tenth of a unit

P=15.2\ units

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