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

Lesson 9-1

Area of

2-D Shapes

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

Squares and Rectangles

s

sA = s²

6

6A = 6² = 36 sq. units

L

WA = LW

12

5

A = 12 x 5 = 60 sq. units

Example:Example:

Area of Rectangle: A = LWArea of Square: A = s²

Lesson 9-1: Area of 2-D Shapes 3

Circles and Sectors2

360

arcSector Area r

r

9 cm

A = (9)² = 81 sq. cm2120

9 27 .360

A sq cm

Area of Circle: A = r²

arc

rB C

A

120°

Example: Example:

9 cm

Lesson 9-1: Area of 2-D Shapes 4

Triangles and Trapezoids1

2Area of Triangle A bh

h hh

b b b1

b2

1 2

1( )

2Area of Trapezoid A h b b

h is the distance from a vertex of the triangle perpendicular to the opposite side.

h is the distance from b1 to b2, perpendicular to each base

Lesson 9-1: Area of 2-D Shapes 5

Example: Triangles and Trapezoids

1

2A bh

7

6

8

12

6

1 2

1( )

2A h b b

16 7 21 .

2A sq units

18(6 12) 72 .

2A sq units

Lesson 9-1: Area of 2-D Shapes 6

Parallelograms & RhombiArea of Parallelogram: A = b h

6

9

A = 9 x 6 = 54 sq. units

8

10

A = ½ (8)(10) = 40 sq units

1 2

1hom :

2Area of R bus A d d

h

b

2d1d

Example: Example:

Lesson 9-1: Area of 2-D Shapes 7

Area of Regions

8

10

12

4 14

8

The area of a region is the sum of all of its non-overlapping parts.

A = ½(8)(10)

A= 40

A = (12)(10)

A= 120

A = (4)(8)

A=32

A = (14)(8)

A=112

Area = 40 + 120 + 32 + 112 = 304 sq. units

Lesson 9-1: Area of 2-D Shapes 8

Areas of Regular Polygons

Perimeter = (6)(8) = 48

apothem =

Area = ½ (48)( ) = sq. units

8

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).

4 34 3

4 3 96 3