1. Perimeter and Area with Polynomial Expressions
August 18, 2016

2. Essential Question
How do I use polynomials to find the area or perimeter of a polygon?

3. Outline
Perimeter
Area
Examples

4. Perimeter Measurement around the polygon (side + side + side +side)
10 cm
12.5 cm
12.5 cm
8 cm
8 cm
10 cm
12.5 cm
10 cm + 8 cm + 10 cm + 8 cm = 36 cm
12.5 cm cm cm = 37.5 cm

5. Perimeter The same concept applies when using polynomial expressions.
2x2 + 2x
2x2
2x2
2x2 + 4x
(2x2 + 2x) + (2x2) + (2x2 + 4x) + (2x2) = 8x2+ 6x

6. Area Measure of the inside of a polygon (i.e. (A=L * W)) 20 cm 10 cm
20 cm * 10 cm = 200 cm2

7. AREA Here’s an example of an area question with polynomials (x+ 2) 2x
2x (x+2) = 2x2 + 4x

8. Examples
Find the perimeter of the figure below.
x2+3x
x+3
x+3
x2+3x

9. Examples x2+3x x+3 x+3 x2+3x Perimeter = side + side + side + side =
(x+3) + (x2 + 3x) + (x+3) + (x2 + 3x) = 2x2 +8x +6

10. Examples
Find the area of the figure below.
2x+3
x2+9

11. Examples Area = length x width = (2x+3)(x2+9) = 2x3 + 18x + 3x2 +27

12. Examples
Find the area of the figure below. x
x+2
x+4
2x+6

13. Examples x+4 2x+6 x x+2 Area of big rectangle= length x width
Area of small rectangle= length x width
(x)(x+2) = x2+2x

14. Examples x
x+2
x+4
2x+6
Subtract area of small rectangle from big rectangle= (2x2+14x+24) – (x2+2x)
= (2x2+14x+24) + (-x2-2x)
= -x2 -2x
= x2+12x +24