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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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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