AF3.1 Use variables in expressions describing geometric quantities (e.g.,
16
Holt CA Course 1 10-1 Perimeter 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: AF1.1, AF1.2, AF3.2 California Standards 1 2
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California Standards. AF3.1 Use variables in expressions describing geometric quantities (e.g., P = 2 w + 2 l , A = bh , C = p d – the formulas for the perimeter of a rectangle, the area of a triangle, and the circumference of a circle, respectively). - PowerPoint PPT Presentation
Transcript of AF3.1 Use variables in expressions describing geometric quantities (e.g.,
Holt CA Course 1
10-1Perimeter
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: AF1.1, AF1.2, AF3.2
California Standards
1 2
Holt CA Course 1
10-1Perimeter
Vocabulary
perimeter
Holt CA Course 1
10-1Perimeter
The perimeter of a polygon is the sum of the lengths of its sides.
Holt CA Course 1
10-1Perimeter
Additional Example 1: Finding the Perimeter of a Polygon
Find the perimeter of the figure.
2.8 + 3.6 + 3.5 + 3 + 4.3
Add all the side lengths.
The perimeter is 17.2 in.
Holt CA Course 1
10-1Perimeter
Check It Out! Example 1
Find the perimeter of the figure.
3.3 + 3.3 + 4.2 + 4.2 + 3
Add all the side lengths.3.3 in. 3.3 in.
4.2 in.4.2 in.
3 in.
The perimeter is 18 in.
Holt CA Course 1
10-1Perimeter
Holt CA Course 1
10-1PerimeterAdditional Example 2: Using a Formula to Find
Perimeter
Find the perimeter P of the parallelogram.
P = 2l+ 2w
Substitute 12 for l and 3 for w.P = (2 • 12) + (2 • 3)
P = 24 + 6
P = 30
Multiply.
Add.
The perimeter is 30 cm.
12 cm
3 cm
Holt CA Course 1
10-1PerimeterCheck It Out! Example 2
Find the perimeter P of the parallelogram.
P = 2l + 2w
Substitute 15 for l and 2 for w.P = (2 • 15) + (2 • 2)
P = 30 + 4
P = 34
Multiply.
Add.
The perimeter is 34 cm.
15 cm
2 cm
Holt CA Course 1
10-1Perimeter
A. What is the length of side a if the perimeter equals 1,471 mm?
P = sum of side lengths
Use the values you know.1,471 = 416 + 272 + 201 + 289 + a
1,471 = 1,178 + a
1,471 – 1,178 = 1,178 + a – 1,178
Add the known lengths.
Subtract 1,178 from both sides.293 = a
Side a is 293 mm long.
Additional Example 3: Finding Unknown Side Lengths and the Perimeter of a Polygon
Find each unknown measure.
Holt CA Course 1
10-1PerimeterAdditional Example 3: Finding Unknown Side
Lengths and the Perimeter of a Polygon
Find each unknown measure.
B. What is the perimeter of the polygon?
Step 1: Find b.
Find the sum of the lengths opposite side b.
b = 50 + 22
b = 72
P = 72 + 55 + 50 + 33 + 22 + 22
P = 254
Step 2: Find the perimeter.
The perimeter of the polygon is 254 cm.
Holt CA Course 1
10-1Perimeter
l = 4w Find the length.
l = (4 • 19)
l = 76
Substitute 19 for w.
Multiply.
Additional Example 3: Finding Unknown Side Lengths and the Perimeter of a Polygon
C. The width of a rectangle is 19 cm. What is the perimeter of the rectangle if the length is 4 times the width?
4w
19 cm
Holt CA Course 1
10-1PerimeterAdditional Example 3C Continued
P = 2l + 2w
Substitute 76 and 19.P = 2(76) + 2(19)
P = 152 + 38
P = 190
Multiply.
Add.
Use the formula for the perimeter of a rectangle.
The perimeter of the rectangle is 190 cm.
4w
19 cm
Holt CA Course 1
10-1PerimeterCheck It Out! Example 3
Find each unknown measure.
A. What is the length of side a if the perimeter equals 1,302 mm?
P = sum of side lengths
Use the values you know.1,302 = 212 + 280 + 250 + 240 + a
1,302 = 982 + a
1,302 – 982 = 982 + a – 982
Add the known lengths.
Subtract 982 from both sides.320 = a
Side a is 320 mm long.
212 mm 280 mm
a250 mm
240 mm
Holt CA Course 1
10-1Perimeter
P = 14 + 12 + 8 + 4 + 6 + 16
P = 60
The perimeter of the polygon is 60 m.
Check It Out! Example 3
Find each unknown measure.
B. What is the perimeter of the polygon?12 m
14 m
b m
8 m
6 m4 m
16 m
Step 1: Find b.
Find the sum of the lengths opposite side b.
b = 12 + 4
b = 16
Step 2: Find the perimeter.
Holt CA Course 1
10-1Perimeter
l = 5w Find the length.
l = (5 • 13)
l = 65
Substitute 13 for w.
Multiply.
Check It Out! Example 3
C. The width of a rectangle is 13 cm. What is the perimeter of the rectangle if the length is 5 times the width?
5w
13 cm
Holt CA Course 1
10-1PerimeterCheck It Out! Example 3C Continued
65 cm
13 cm
P = 2l + 2w
Substitute 65 and 13.P = 2(65) + 2(13)
P = 130 + 26
P = 156
Multiply.
Add.
Use the formula for the perimeter of a rectangle.
The perimeter of the rectangle is 156 cm.
