Circumference SPI 21B: solve equations to find length, width, perimeter and area SPI 32L: determine the area of indicated regions involving figures SPI 41A: determine the perimeter & area of 3 or 4 sided plane figures Objectives: • Find the area and perimeter of irregular geometric figures • Find the area and perimeter of regular geometric figures • Apply area and perimeter formulas to real world situations • Discover relationships between different geometric figures • Find Volume of rectangular solids Outline of Lesson Vocabulary Common formulas for geometric figures Irregular geometric figures Volume of Rectangular Solids
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Objectives: Find the area and perimeter of irregular geometric figures
Section 1-7 Perimeter, Area, Circumference SPI 21B: solve equations to find length, width, perimeter and area SPI 32L: determine the area of indicated regions involving figures SPI 41A: determine the perimeter & area of 3 or 4 sided plane figures. - PowerPoint PPT Presentation
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Section 1-7 Perimeter, Area, Circumference SPI 21B: solve equations to find length, width, perimeter and areaSPI 32L: determine the area of indicated regions involving figuresSPI 41A: determine the perimeter & area of 3 or 4 sided plane figures
Objectives:• Find the area and perimeter of irregular geometric figures• Find the area and perimeter of regular geometric figures• Apply area and perimeter formulas to real world situations• Discover relationships between different geometric figures• Find Volume of rectangular solids
Outline of LessonVocabularyCommon formulas for geometric figuresIrregular geometric figuresVolume of Rectangular Solids
Perimeter: • the sum of the lengths of the sides of a polygon• fence around a plot of land
Circumference: • the distance around the outside of a circle• the distance around the earth
Area:• number of units (squared) enclosed by the perimeter
Amount of carpet needed for a room
• number of units enclosed by the circumference (circle)
Amount of material needed to construct a trampoline
Base: bottom of a figure
Height/Altitude: line perpendicular to base extending to the top of the figure
base
height
Diameter: a straight line connecting the center of a circle with two points on its perimeter
Radius: the length of a line segment between the center and circumference of a circle
Some Common Formulas
SquarePerimeter: P = 4s
Area: A = s2
RectanglePerimeter: P = 2b + 2h
Area: A = bhb = baseh = height
s = side
h
b
Circle
d = diameterr = radius
Circumference: C = d or C = 2r
Area: A = r2
Triangle
b = baseh = height
Perimeter: use the distance formula
Area: A = ½ bh
Some Common Formulas (cont)
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?
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?
AB + BC + AC = 6 + 8 + 10 = 24. The perimeter is 24 units.
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.
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
Estimate the area of an Irregular Geometric Figure
• Count the number of square units, by marking the diagram
• Estimate partial units
• Combine partial units to create whole units
• Add the units to estimate area
Finding Area of Irregular Figures
.5
.5
Estimate the Area of the Irregular Geometric Figure
Mark all the whole units 1 1 1
1 1 1
1 1 1
1 1 1
1 1 1 1 1 1
1 1
1 1
1 1Mark the partial units• estimate
1
1
The area is approximately 27 units2
Volume of Rectangular Solids
Volumethe amount of 3-dimensional space occupied by an object
How much product a box of cereal
contains
Volume FormulaV = lwh
Apply Volume Formula of Rectangular Solids
A die is a cube molded from hard plastic. The edge of a typical die measures 0.62 in. Dice are usually produced in a mold which holds 100 die at one time. To the nearest cubic inch, how much plastic is needed to fill this large mold?
V = l · w · h = (.62)(.62)(.62) = .238 in3
For 100 dice = 100 x .238 = 23.8 or approximately 24 cubic inches