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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

4. Perimeter and Area in the Coordinate Plane

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Exercise 14 Page 410

Use the Distance Formula and the Ruler Postulate.

P ≈ 16.94 units.

Practice makes perfect

The given polygon has six sides, AB, BC, CD, DE, EF, and FA. Four of these sides are either vertical or horizontal, so for these cases we can use the Ruler Postulate. Let's start with BC.

BC=|y_2-y_1|

y_2= - 2, y_1= 0

BC=| - 2 - 0|

Subtract term

BC=|- 2|

|-2|=2

BC=2

We can do all four vertical and horizontal sides of the polygon in the same way.

Side	Coordinates	\|x_2-x_1\| or \|y_2-y_1\|	Length
BC	(2,0) (2,- 2)	\|y_2-y_1\|→ \| - 2- 0\|	2
CD	(2,- 2) (0,- 2)	\|x_2-x_1\|→ \| 0- 2\|	2
EF	(- 2,2) (- 2,4)	\|y_2-y_1\|→ \| 4- 2\|	2
FA	(- 2,4) (0,4)	\|x_2-x_1\|→ \| 0-( - 2)\|	2

For the remaining two sides, we will need to use the Distance Formula. Let's start with AB.

AB = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)

SubstitutePoints

Substitute ( 2,0) & ( 0,4)

AB = sqrt(( 2- 0)^2 + ( 0- 4)^2)

Subtract terms

AB=sqrt(2^2+(- 4)^2)

Calculate power

AB=sqrt(4+16)

Add terms

AB=sqrt(20)

We will find the length of DE in the same way, giving us both of our remaining side lengths.

Side	Coordinates	sqrt((x_2-x_1)^2+(y_2-y_1)^2)	Length
AB	(0,4) (2,0)	sqrt(( 2- 0)^2+( 0- 4)^2)	sqrt(20)
DE	(0,-2) (-2,2)	sqrt(( -2- 0)^2+( 2-( -2))^2)	sqrt(20)

We can now calculate the perimeter which is the sum of the length of the sides.

P=AB + BC + CD + DE + EF + FA

SubstituteValues

Substitute values

P= sqrt(20) + 2 + 2 + sqrt(20) + 2 + 2

Use a calculator

P = 16.94427...

Round to 2 decimal place(s)

P ≈ 16.94

The polygon's perimeter is P ≈ 16.94 units.

Subchapter links

Communicate Your Answer p.405

Monitoring Progress p.406-409

Exercises p.410-412