Jim Smith JCHS Expand analysis of units of measure to include area and volume Use right triangle trigonometry to find the area and perimeter of quadrilaterals Derive and use the formulas for the area and perimeter of a regular polygon.

PERIMETER There are many formulas (or shortcuts) for finding the perimeter of polygons. The only one you need to remember is…. ADD ALL SIDES This will work for all polygons

P= =22P= =25 P= 9+9+4=22 P= =31

Area of Rectangles Think of filling the rectangle with boxes. All answers should be in square units Columns By 3 Rows 4X3= 12 This is the length times the width A= lw

A=lw A=51x5 A=255 sq units A=lw A=38x12 A=456 sq units Rectangles

Area of Parallelograms h b A=bh The height must form a right angle with a base

A=bh A=10x7 A=70 sq. units A=bh A=15x6 A=90 sq. units Parallelograms

Area of Triangles bb h h A=1/2 bh

Triangles 21 7 A = ½ bh A = ½ 7x21 A = ½ 147 A = A = 73½ A = 73.5 sq units

Right Triangle Equilateral or Isosceles Triangle 6 8 A = ½ bh A = ½ 6 x 8 A = 24 Sq. Unit 10 60° 55 5√35√3 A = ½ bh A = ½ 10 x 5√3 A = 25√3 Sq. Unit

Area of Trapezoids b1b1 b2b2 h A = ½ h( b 1 + b 2 )

A = ½ h(b 1 + b 2 ) A = ½ (6)( 8+12 ) A = 3( 20 ) A = 60 sq units Trapezoid

45° A = ½ h(b 1 + b 2 ) A = ½ 6( 8+14 ) A = ½ 6(22) A = 66 sq units Trapezoid with 45° 45° 6

60° ° 5√35√3 5 A=1/2 h( b 1 +b 2 ) A= ½ 5√3 ( 6+16 ) A= ½ 5√3 ( 22 ) A= 5√3 ( 11 ) A= 55√3 sq units Isosceles Trapezoid

Area of Rhombi and Kites d1d1 d2d2 A = ½ d 1 x d 2 d2d2 d1d1 ( d 1 and d 2 are the whole diagonals )

Rhombus and Kite 10 8 X A = ½ d 1 x d 2 A = ½ 12x16 A = 96 sq units A = ½ d 1 x d 2 A = ½ 8x10 A = 40 sq units

Area of Regular Polygons s r a s = side a = apothem r = radius A=1/2 aP

²+x² = 5² A = ½ aP A = ½ 4x36 A = 72 sq units P = 6x6 P = 36 Regular Hexagon

The area of any figure is the sum of all the non-overlapping parts Trapezoid Triangle Rectangle

+ + + Add The Parts OR

Complete the figure and subtract the part you don’t want ( bake the cake and eat the part you don’t want! )