Perimeter

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Perimeter AREA of POLYGONS
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Perimeter of a Polygon To calculate the
perimeter of a polygon, we need to determine the
length of all of its sides and add together.
Area of a Polygon To calculate the area of a
polygon, we need to determine the length of
certain dimensions. These will depend on the
shape and the formula that we use to calculate
area.
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Calculating the length of sides will involve
intersecting equations to find vertices.
Calculating dimensions such as height will
involve determining the distance between a point
(a vertex) and a line (a base).
EXAMPLE Determine the perimeter and area of the
triangle.
Find vertex A y x 3 ? y 3x 1
x 3 3x 1 x 3x 1 3 -2x -2 x 1
Find vertex C y -2x - 3 ? y 3x 1
-2x - 3 3x 1 -2x 3x 1 3 -5x 4 x -0.8
y x 3 y 1 3 y 4 A(1, 4)
y 3x 1 y 3(-0.8) 3 y -2.4 3 y 0.6
C(-0.8, 0.6)
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Find vertex B y x 3 ? y -2x - 3
x 3 -2x - 3 x 2x -3 3 3x -6 x -2
y x 3 y (-2) 3 y 1 B(-2,1)
Perimeter 4.24 1.26 3.85 9.35 units
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AREA The formula for area requires us to use
the base and height of the triangle. Either side
can be used as a base. We will use side AC. We
need to find the equation of the height from that
base.
b 3.85 units
h ? units
Slope of base 3
Equation of height
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Instead of carrying out the last few steps, the
height from B could have been determined using
the following formula
y 3x 1 0 3x y 1 (x1,y1) (-2,1) A 3
B -1 C 1
b 3.85 units
h 1.90 units
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The height of a parallelogram or a trapezoid
refers to the distance between the parallel sides
(bases).
Calculate the area of the following trapezoid.
1. We must determine the ordered pairs for each
vertex because you need to calculate the length
of both bases.
2. We must determine the equation of the height
(DH) so that you can identify the ordered pair
for H.
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Find A
A (2,-3)
Find B
3(x 5) -2x 5 3x 15 -2x 5 5x -20 x
-4
y x 5 y -4 5 y 1 B (-4,1)
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Find C
y x 5 y -1.6 5 y 3.4 C (-1.6,3.4)
3(x 5) -2x 7 3x 15 -2x 7 5x -8 x
-1.6
Find B
D (2,1)
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Height from D (2,1)
Equation of AB
3y -2x 5 2x 3y 5 0 (x1,y1)
(2,1) A 2 B 3 C 5