holt ca course 1 10-3 area of parallelograms af3.1 use variables in expressions describing geometric...
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Holt CA Course 1
10-3Area of Parallelograms
AF3.1 Use variables in expressions describing geometric quantities (e.g.,P = 2w + 2l, A = bh, C = d–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
California Standards
1 2
Holt CA Course 1
10-3Area of Parallelograms
Vocabulary
area
base
height
Holt CA Course 1
10-3Area 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.
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.
h
b
Area = 15 square units
Holt CA Course 1
10-3Area of Parallelograms
Holt CA Course 1
10-3Area of Parallelograms
Find the area of the parallelogram.
Additional Example 1: Finding the Area of a Parallelogram
8 m
16 m
A = bh
A = 16· 8
A = 128
The area of the parallelogram is 128 m2.
Use the formula.
Substitute for b and h.
Multiply.
Holt CA Course 1
10-3Area of Parallelograms
Find the area of the parallelogram.
6 cm
12 cm
A = bh
A = 12· 6
A = 72
The area of the parallelogram is 72 cm2.
Check It Out! Example 1
Use the formula.
Substitute for b and h.
Multiply.
Holt CA Course 1
10-3Area of Parallelograms
Find the area of the rectangle.
Additional Example 2: Finding the Area of a Rectangle
4.5 in.
7.4 in.
A = lw
A = 7.4 · 4.5
A = 33.3
The area of the rectangle is 33.3 in2.
Use the formula.
Substitute for l and w.
Multiply.
Holt CA Course 1
10-3Area of Parallelograms
Find the area of the rectangle.
6.3 in.
8.2 in.
A = lw
A = 8.2 · 6.3
A = 51.66
The area of the rectangle is 51.66 in2.
Use the formula.
Substitute for l and w.
Multiply.
Check It Out! Example 2
Holt CA Course 1
10-3Area of Parallelograms
The area of a playing field is 1,470 ft2 and the length is 42 ft. What is the width of the field?
Additional Example 3: Finding Length or Width of a Rectangle
A = lw
1,470 = 42 · w
=
The width of the playing field is 35 ft.
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.1,47042
42 · w 42
35 = w
Holt CA Course 1
10-3Area of Parallelograms
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?
Check It Out! Example 3
A = lw
3,570 = l · 70
=
The length of the parking lot is 51 ft.
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.3,57070
l · 70 70
51 = l
Holt CA Course 1
10-3Area of Parallelograms
A carpenter is laying a wood floor measuring 4 yd by 5 yd. How many square feet of flooring material does she need?
Additional Example 4: Measurement Application
Step 1: Draw and label a diagram.
The wood floor is measured is yards, but the answer should be in feet.
4 yd · = 12 ft
5 yd · = 15 ft
Step 2: Convert the units.4 yd
5 yd
3 ft 1 yd
3 ft 1 yd
Convert yards to feet by multiplying by a ratio equal to 1.
Holt CA Course 1
10-3Area of Parallelograms
A carpenter is laying a wood floor measuring 4 yd by 5 yd. How many square feet of flooring material does she need?
Additional Example 4 Continued
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
10-3Area of Parallelograms
A carpenter is laying a tile floor measuring 5 yd by 7 yd. How many square feet of tile material does she need?
Check It Out! Example 4
Step 1: Draw and label a diagram.
The tile floor is measured is yards, but the answer should be in feet.
5 yd · = 15 ft
7 yd · = 21 ft
Step 2: Convert the units.
5 yd
7 yd
3 ft 1 yd
3 ft 1 yd
Convert yards to feet by multiplying by a ratio equal to 1.
Holt CA Course 1
10-3Area of ParallelogramsCheck It Out! Example 4 Continued
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.
A carpenter is laying a tile floor measuring 5 yd by 7 yd. How many square feet of tile material does she need?