Perimeter and Area with Polynomial Expressions August 18, 2016

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

Outline Perimeter Area Examples

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 + 12.5 cm + 12.5 cm = 37.5 cm

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

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

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

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

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

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

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

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

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

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