The document discusses the formulas to calculate the area of various 2-D shapes: - The area of a square is s^2, and the area of a rectangle is length x width. - The area of a circle is πr^2, and the area of a sector is (arc length/360)πr^2. - The area of a triangle is 1/2 base x height, and the area of a trapezoid is 1/2(b1 + b2) x height. - The area of a parallelogram is base x height, and the area of a rhombus is 1/2 diagonal 1 x diagonal 2. - The

1. Lesson 9-1
Area of
2-D Shapes
Lesson 9-1: Area of 2-D Shapes 1

2. Squares and Rectangles
Area of Square: A = s² Area of Rectangle: A = LW
A = s² A = LW W
s
s Example: L
Example:
A = 6² = 36 5
6 sq. units
12
6 A = 12 x 5 = 60 sq. units
Lesson 9-1: Area of 2-D Shapes 2

3. Circles and Sectors
arc
Area of Circle: A = π r² Sector Area = π r2
360o
A
9 cm 120°
9 cm
arc
r B r C
Example: Example:
120
A = π(9)² = 81 π sq. cm A= π g = 27π sq.cm
9 2
360
Lesson 9-1: Area of 2-D Shapes 3

4. Triangles and Trapezoids
1 1
Area of Triangle A = bh Area of Trapezoid A = h(b1 + b2 )
2 2
h is the distance from a h is the distance from b1 to b2,
vertex of the triangle perpendicular to each base
perpendicular to the opposite
side.
b2
h
h
h
b b b1
Lesson 9-1: Area of 2-D Shapes 4

5. Example: Triangles and Trapezoids
1 1
A = bh A = h(b1 + b2 )
2 2
12
8
7
6
6
1 1
A = • 6 • 7 = 21 sq.units A = 8(6 + 12) = 72 sq.units
2 2
Lesson 9-1: Area of 2-D Shapes 5

6. Parallelograms & Rhombi
Area of Parallelogram: A = b h Area of R hom bus : A =
1
d1d 2
2
h d1
d2
b
8
Example: Example:
6
10
9
A = 9 x 6 = 54 sq. units A = ½ (8)(10) = 40 sq units
Lesson 9-1: Area of 2-D Shapes 6

7. Area of Regions
The area of a region is the sum of all of its non-overlapping parts.
10 8
4 14
8 12
A = ½(8)(10) A = (12)(10) A = (4)(8) A = (14)(8)
A= 40 A= 120 A=32 A=112
Area = 40 + 120 + 32 + 112 = 304 sq. units
Lesson 9-1: Area of 2-D Shapes 7

8. Areas of Regular Polygons
If a regular polygon has an area of A square units, a
perimeter of P units, and an apothem of a units, then
A = ½ (a)(p).
Perimeter = (6)(8) = 48
8
apothem = 4 3
4 3
Area = ½ (48)( 4 3 ) = 96 3sq. units
Lesson 9-1: Area of 2-D Shapes 8