10.1 Areas of Parallelograms and Triangles
March 29, 2010
10.1 Areas of Parallelograms & Triangles
(AND MORE)
Objective: Find the areas of basic polygons.
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10.1 Areas of Parallelograms and Triangles
March 29, 2010
What is area?
Area is measuring the amount of squares inside an object.
What is the area of this rectangle?
15 square units
Shortcut for counting the number of squares:
Multiply the length and width (or base and height)
Apr 3­11:57 AM
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10.1 Areas of Parallelograms and Triangles
March 29, 2010
Rectangle
A = b(h)
Example: Find the area
15
A = 15(10)
A = 150 units2
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Note: A square is also a rectangle.
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10.1 Areas of Parallelograms and Triangles
March 29, 2010
Parallelogram
*You can't cut this shape into
perfect square units, so how are
we going to find the area?
*A triangle can be cut from one side
and moved to the other side to form
a rectangle. So we find the area the
same way as a rectangle.
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10.1 Areas of Parallelograms and Triangles
March 29, 2010
Parallelogram
A = b(h)
h
b
*Note: Height is always perpendicular
to the base not matter what shape we
are talking about.
Example: Find the area.
A = b(h)
A = 3(7)
3 cm
A = 21 cm2
7 cm
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10.1 Areas of Parallelograms and Triangles
March 29, 2010
Triangle
*Again you can't cut this shape into
perfect square units, so how are
we going to find the area?
*The current triangle can be rotated
180o about the midpoint of a side to
create a parallelogram. Therefore, the
area of a triangle is half the area of a
parallelogram.
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10.1 Areas of Parallelograms and Triangles
March 29, 2010
Triangle
A = 1/2(b)(h)
h
b
A = b(h)
2
h
b
h
b
h
b
*Base & height make a right angle!
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10.1 Areas of Parallelograms and Triangles
March 29, 2010
Triangle
Example: Find the area
A = 1/2(8)(12)
12 ft
A = 4(12)
A = 48 ft2
8 ft
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10.1 Areas of Parallelograms and Triangles
March 29, 2010
Trapezoid
A trapezoid has at least one pair of parallel sides, they are the two bases.
b2
We can find the area of a trapezoid by
cutting it into two triangles. We can
find the area of each triangle and add
them together.
b1
b2
Areatrapezoid = Areatriangle 1 + Areatriangle 2
triangle 2
triangle 1
b1
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10.1 Areas of Parallelograms and Triangles
March 29, 2010
Trapezoid
b2
Areatriangle 1 = 1/2(b1)(h)
triangle 2
h
triangle 1
b1
Areatriangle 2 = 1/2(b2)(h)
Areatrapezoid = 1/2(b1)(h) + 1/2(b2)(h)
Area of a Trapezoid (simplified):
A = 1/2(h)(b1 + b2)
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10.1 Areas of Parallelograms and Triangles
March 29, 2010
Trapezoid
A = 1/2(h)(b1 + b2)
Example: Find the area
7m
A = 1/2(4)(9 + 7)
A = 2(16)
4
9m
A = 32 m2
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10.1 Areas of Parallelograms and Triangles
March 29, 2010
Circle
A circle has a diameter and a radius.
The diameter is a straight line passing through the center of the circle
meeting the edge of the circle at each end.
The radius is a straight line extending from the center of the circle to
the edge of the circle.
radius
diameter
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10.1 Areas of Parallelograms and Triangles
March 29, 2010
Circle
A = πr2
Example: Find the area
r = 10.5/2
r = 5.25
A = π(5.25)2
A = 86.59 in.2
10.5 in.
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10.1 Areas of Parallelograms and Triangles
March 29, 2010
Homework:
Practice #1
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