section 1-7 perimeter, area, circumference objectives: find perimeter and area of rectangles and...
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Section 1-7 Perimeter, Area, Circumference
Objectives:• find perimeter and area of rectangles and squares• find circumference and area of circles
Perimeter: • the sum of the lengths of the sides of a polygon• fence around a garden
Circumference: • the distance around the outside of a circle
Area:• number of units (squared) enclosed by the perimeter or circumference
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Some Common Formulas
SquarePerimeter: P = 4s
Area: A = s2
RectanglePerimeter: P = 2b + 2h
Area: A = bhb = baseh = height
s = side
Circle
d = diameterr = radius
Circumference: C = d or C = 2r
Area: A = r2
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Real-World Connection
Fencing. Your pool is depicted in the diagram below. You want to build a fence around the deck. How much fencing will you need?
Width of pool and deck: 15 + 3 + 3 = 21 feet
Length of pool and deck: 20 + 3 + 3 = 26 feet
Solve:P = 2w + 2L Formula = 2(21) + 2(26) Substitute = 94 Simplify
You will need 94 feet of fencing.
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Real-World and Finding Circumference
Biology. In the Pacific Northwest, a red fox has a circular home range with a radius of about 718 meters. What is the area of the home range of a red fox?
A = r2 FormulaA = (718) 2 Substitute = 1,619,566 Simplify
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Finding Perimeter in the Coordinate Plane
Find the perimeter of ∆ABC.
Find the length of each side.
Side AB. |5 – (-1)| = 6
Side BC. |6- (-2)| = 8
Side AC.
AB + BC + AC = 6 + 8 + 10 = 24. The perimeter is 24 units.
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Finding Area of a Rectangle
You are designing a banner for a music festival. The banner will be 4 ft wide by 7 feet high. How much material will you need?
Area of Rectangle = bh
Convert yards to feet: 7 yards = 21 feet
Substitute values into formula
A = 4(21) = 84
You will need 84 square feet (ft2) of material.
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Finding Area of Irregular Figures
Find the area of the figure.
Separate the figure into rectangles.
Use Area of a Rectangle Formula
A1 = 6 ∙ 2 = 12
A2 = 4 ∙ 2 = 8
A3 = 2 ∙ 2 = 4
Total Area = 12 + 8 + 4 = 24 cm2