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Mathematicians have created formulas to help you find the perimeter and areas of different shapes. Use the formulas to solve your problems!
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PerimeterAny shape’s “perimeter” is the distance on
the outside of the shape…like a fence around a yard.
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PerimeterTo calculate the perimeter of any shape, just add up each line segment of the “fence” around the shape.
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PerimeterTriangles have 3 sides…add up each sides length.
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88
88+8+8=24The Perimeter is 24
Practice: Find the perimeter1)
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53
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So add up 3 + 4 + 5 = 12 units
PerimeterA square has 4 sides of a fence
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12 12
12
12
12+12+12+12=48
PerimeterSometimes, problems may only give you two
measurements for a square or rectangle.No problem. Remember that all the sides of a
square is the same measure and the opposite sides of a rectangle are the same measure.
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RememberSquares ALL sides are equal…so if they
give you one side, you know ALL the sidesLength=the Largest sideIf they “leave” numbers out, they are equal
to their opposite side.
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The Same!!If the bottom is 15…the top is…
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Square/Rectangle FormulaPerimeter=2L + 2W or 2(L + W) P= 2(5) + 2(4) P=2(5 + 4)P= 10+8 P= 2(9)P= 18 P=18Or just ADD the 4 sides!!
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510
Other shapesJust add up EACH segment
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10
8 sides, each side 10 so 10+10+10+10+10+10+10+10=80
10
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Circumference of a CirclePerimeter/Circumference = pi x diameterPi is always 3.14 or 3 (for estimation)Circumference is a fancy name for
perimeterThe diameter is a line from one side to
the other side of a circle through its origin (It’s twice the radius)
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If the radius is 5, then the diameter is 10
Practice:Use the formula C = πd
Find the circumference of this circle with a diameter of 10 cm.
D = 10 so multiply (10)(3.14) = 31.4 cm
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AreaArea is the ENTIRE INSIDE of a shapeIt is always measured in “squares”
(square inch, or square feet or whatever unit…)
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AREASquare units means that “that” many squares fit inside that shape (if
measured in feet…it’s feet…if meters…it’s meters. In this example the area is 4 square units…note 4 squares fit)
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2 units (ft, in, m)
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3 4
Area of Squares/RectanglesLength x Width=Area
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2
Length(2) xWidth(2) = 4 square units
Parallelogram AreaSame idea as squares & rectangles, but they change the words to Base (length: bottom of shape) and height (similar to width but MUST be 90 degrees to the base.)
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Parallelogram AreaArea=Base x Height
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BASE (length)
Height (width)
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5
Base 8 x Height 5 = Area 40
The diagonal line is NOTthe height!!!
Formula for area of squaresArea= S^2Area= Side x Side (side squared) (just a
different way of saying length x width)
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Side one
Side two
Different Names/Same ideaLength x Width = Area
Side x Side = Area
Base x Height = Area (Height must be 90 degrees to the base. NOT the slanted side’s length.)
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Area of a Triangle½ Base x Height = Area(It’s ½ because ½ of the “square” is
missing)
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Base
Height
Height
Base
8
5
½ Base x Height = Area½ (8) x 5 = Area 4 x 5 = 20
Area of a Circle
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Area of a circle
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Radius
5
Area=3.14 x (5 x 5) Perimeter = 3.14 x 10
For most tests you will have the formulas
given to you. Just remember which one to use for which shape and you’ll do fine.
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