Transcript Slide 1

10-3 Area of Parallelograms
California
Standards
AF3.1 Use variables in expressions
describing geometric quantities (e.g.,
P = 2w + 2l, A = 12bh, C = pd–the formulas
for the perimeter of a rectangle, the area of
a triangle, and the circumference of a circle,
respectively).
Also covered: NS2.1,
AF1.1,
AF2.1, AF3.2
Holt CA Course 1
10-3 Area of Parallelograms
Vocabulary
area
base
height
Holt CA Course 1
10-3 Area of Parallelograms
The area of a figure is the number
of non-overlapping unit squares
needed to cover the figure. Area is
measured in square units.
Area = 15 square units
The base of a parallelogram is the length of
one side. Its height is the perpendicular
distance from the base to the opposite side.
For a rectangle, the base is the
same as the length, and the height
is the same as the width.
Holt CA Course 1
h
b
10-3 Area of Parallelograms
Holt CA Course 1
10-3 Area of Parallelograms
Additional Example 1: Finding the Area of a
Parallelogram
Find the area of the parallelogram.
A = bh
8m
16 m
Use the formula.
A = 16· 8 Substitute for b and h.
A = 128
Multiply.
The area of the parallelogram is 128 m2.
Holt CA Course 1
10-3 Area of Parallelograms
Check It Out! Example 1
Find the area of the parallelogram.
A = bh
6 cm
12 cm
Use the formula.
A = 12· 6 Substitute for b and h.
A = 72
Multiply.
The area of the parallelogram is 72 cm2.
Holt CA Course 1
10-3 Area of Parallelograms
Additional Example 2: Finding the Area of a
Rectangle
Find the area of the rectangle.
4.5 in.
7.4 in.
A = lw
A = 7.4 · 4.5
A = 33.3
Use the formula.
Substitute for l and w.
Multiply.
The area of the rectangle is 33.3 in2.
Holt CA Course 1
10-3 Area of Parallelograms
Check It Out! Example 2
Find the area of the rectangle.
6.3 in.
8.2 in.
A = lw
A = 8.2 · 6.3
A = 51.66
Use the formula.
Substitute for l and w.
Multiply.
The area of the rectangle is 51.66 in2.
Holt CA Course 1
10-3 Area of Parallelograms
Additional Example 3: Finding Length or Width of a
Rectangle
The area of a playing field is 1,470 ft2 and the
length is 42 ft. What is the width of the field?
A = lw
1,470 = 42 · w
1,470 = 42 · w
42
42
35 = w
Use the formula for the area of a
rectangle.
Substitute 1,470 for A and 42 for l.
Divide both sides by 42 to isolate w.
The width of the playing field is 35 ft.
Holt CA Course 1
10-3 Area of Parallelograms
Check It Out! Example 3
The area of a rectangular parking lot is
3,570 ft2 and the width is 70 ft. What is the
length of the parking lot?
A = lw
3,570 = l · 70
3,570 = l · 70
70
70
51 = l
Use the formula for the area of a
rectangle.
Substitute 3,570 for A and 70 for w.
Divide both sides by 70 to isolate l.
The length of the parking lot is 51 ft.
Holt CA Course 1
10-3 Area of Parallelograms
Additional Example 4: Measurement Application
A carpenter is laying a wood floor measuring
4 yd by 5 yd. How many square feet of
flooring material does she need?
Step 1: Draw and label a diagram.
Step 2: Convert the units.
4 yd
5 yd
The wood floor is measured is yards, but the answer
should be in feet.
4 yd · 3 ft = 12 ft Convert yards to feet by
1 yd
multiplying by a ratio
5 yd · 3 ft = 15 ft equal to 1.
1 yd
Holt CA Course 1
10-3 Area of Parallelograms
Additional Example 4 Continued
A carpenter is laying a wood floor measuring
4 yd by 5 yd. How many square feet of flooring
material does she need?
Step 3: Find the area of the floor in square feet.
A = lw
Use the formula for the area of a
rectangle.
A = 12 · 15
Substitute 12 for l and 15 for w.
A = 180
Multiply.
The carpenter needs 180 ft2 of flooring material.
Holt CA Course 1
10-3 Area of Parallelograms
Check It Out! Example 4
A carpenter is laying a tile floor measuring 5
yd by 7 yd. How many square feet of tile
material does she need?
Step 1: Draw and label a diagram.
5 yd
7 yd
Step 2: Convert the units.
The tile floor is measured is yards, but the answer
should be in feet.
5 yd · 3 ft = 15 ft Convert yards to feet by
1 yd
multiplying by a ratio equal
7 yd · 3 ft = 21 ft to 1.
1 yd
Holt CA Course 1
10-3 Area of Parallelograms
Check It Out! Example 4 Continued
A carpenter is laying a tile floor measuring 5
yd by 7 yd. How many square feet of tile
material does she need?
Step 3: Find the area of the tile floor in square feet.
A = lw
Use the formula for the area of a
rectangle.
A = 15 · 21
Substitute 15 for l and 21 for w.
A = 315
Multiply.
The carpenter needs 315 ft2 of tile material.
Holt CA Course 1