1. Chapter 9 Big Ideas
9-1: Area formulas of triangles and quadrilaterals:
Parallelograms
Triangles
Trapezoids
Quadrilaterals w/ diagonals (kite & rhombus)
Find the area of each.
A=½· d1·d2 5
48 12
A=½·h(b1+b2)
tan48 = x/5
5tan48 = x
x  5.6
12²+b²=15²
144+b²=225
b²=81
b=9
15 cm
A=½· 10·17.5
A  87.8 unit²
A=½·12(9+18)
A=6·27
A=162 cm²

2. 9-2: Circles and Regular Polygons Area and circumference of circles
Areas of regular polygons: (apothem and radius)
Find the circumference of a circle whose area is 64 in²
C=2r
A = r²
64 = r²
r² = 64
r = 8
C=2·8·
C = 16 in
Find the area of the regular polygon. (Units are centimeters)
sin22.5=x/10
10sin22.5=x
x 
s 
A = ½·nsa
A = ½·8·
360/(2·8) =22.5
(7.6537)(9.2388)
A= cm²  10
cos22.5=y/10
10cos22.5=y
y  y x

3. 9-3/4: Composite figures and coordinate plane
Find areas by adding or subtracting known figures.
Estimating areas
Approximating a figure
Counting squares
(Pick’s Formula)
Finding area and perimeter of a figure on the coordinate plane.
Finding the area of a quadrilateral using subtraction.
Estimate the area:
Find the area: 1 2 3 4 5 6 7
A= ½bh + bh
A= ½(7)(11.2) + (5.2)(5.2)
A= yd² 8
8 + ½ · 4 = 10

4. Area of rect.- Area of 4 triangles 6
Find the perimeter and area of a figure with the vertices
T(-4,4), U(5,3), V(4,-5), W(-5,1) 
Perimeter: 1 9
3²+1²=c²
10=c²
c=10
9²+1²=c²
82=c²
c=82
8²+1²=c²
65=c²
c=65 1 3
9²+6²=c²
117=c²
c=117
P=10 + 82 + 65 + 117
P=31.1 units 8
Area:
Area of rect.- Area of 4 triangles 6
A = 10 · 9 ̶ ½·1·3 ̶ ½·1·9 ̶ ½·8·1 ̶ ½·6·9
A= 90 ̶ ̶ ̶ 4 ̶ 27
A = 53 sq units 9 1

5. 9-5: Changing Dimensions
Non-proportional changes: Change in area is the product of the changes to the dimensions.
Proportional changes: Sides Perimeter Area
m m m²
What happens to the area of a triangle whose base is doubled?
What happens to the area of a regular polygon whose sides are tripled?
You want to quadruple the area of a rectangular play area. Name three ways you could accomplish this.
Describe the change in area of a circle if its circumference is five times as big.
Area is doubled
Area is 9 times bigger
Area is twenty-five times as big