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HELP ASAP!

Select the correct answer from each drop-down menu.
Consider polygon JKLMNO on the coordinate grid.

Drop-down options
First one 17.07, 12.5, 25
Second 50, 30, 20
Third one 61, 47, 68.5, 37

HELP ASAP Select The Correct Answer From Each Dropdown Menu Consider Polygon JKLMNO On The Coordinate Grid Dropdown Options First One 1707 125 25 Second 50 30 2 class=

Sagot :

The area of the polygon JKLMNO is 68.5 square units

The area of triangle MNO

The coordinates of the triangle are:

M = (-1, -5)

N = (-8, -6)

O = (-5, -2)

Calculate the base and the height of the triangle using:

[tex]d = \sqrt{(y_2 -y_1)^2 +(x_2 -x_1)^2[/tex]

So, we have:

[tex]ON = \sqrt{(-5+ 8)^2 +(-2 + 6)^2[/tex]

ON = 5

[tex]OM = \sqrt{(-5+ 1)^2 +(-2 + 5)^2[/tex]

OM = 5

The area is:

Area = 0.5 * ON * OM

This gives

Area = 0.5 * 5 * 5

Evaluate

Area = 12.5

Hence, the area of the triangle MNO is 12.5 square units

The perimeter of rectangle JLMO

The coordinates of the rectangle are:

J = (1, 6)

L = (5, 3)

M = (-1, -5)

O = (-5, -2)

Calculate the length and the width of the rectangle using:

[tex]d = \sqrt{(y_2 -y_1)^2 +(x_2 -x_1)^2[/tex]

So, we have:

[tex]OM = \sqrt{(-5+ 1)^2 +(-2 + 5)^2[/tex]

OM = 5

[tex]ML = \sqrt{(-1 - 5)^2 + (-5 - 3)^2[/tex]

ML = 10

The perimeter is:

Perimeter = 2 * (OM + ML)

This gives

Perimeter = 2 * (5 + 10)

Evaluate

Perimeter = 30

Hence, the perimeter of the rectangle JLMO is 30 units

The area of the polygon

In (a), we have:

The area of the triangle MNO is 12.5 square units

The area of the rectangle JKMO is:

Area = OM * ML

This gives

Area = 5 * 10 = 50

The coordinates of triangle JKL are:

J = (1, 6)

K = (5, 6)

L = (5, 3)

Calculate the base and the height of the triangle using:

[tex]d = \sqrt{(y_2 -y_1)^2 +(x_2 -x_1)^2[/tex]

So, we have:

[tex]KL = \sqrt{(5- 5)^2 +(3 - 6)^2[/tex]

KL = 3

[tex]JK = \sqrt{(1- 5)^2 +(6 - 6)^2[/tex]

JK = 4

The area of JKL is

Area = 0.5 * KL * JK

This gives

Area = 0.5 * 3 * 4

Area = 6

Add the three areas

Total area = 6 + 12.5 + 50

Evaluate

Total area = 68.5

Hence, the area of the polygon JKLMNO is 68.5 square units

Read more about area and perimeter at:

https://brainly.com/question/11957651

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