10.3 Perimeter and Area
The perimeter of a polygon is the length
around the polygon.
It is the sum of the lengths of the edges
that comprise the polygon.
This is similar to the circumference of a
circle.
5
8
10
The area of a polygon is the amount of
surface area the interior of the polygon
covers.
Perimeter and Area
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Section 10.3, Slide 5
3
2
Find the perimeter of the rectangle.
Find the area of the rectangle.
A parallelogram
can be
converted to a
rectangle from a
triangle that has
been cut off and
moved to the
other side.
Knowing the
area of a
rectangle gives
the area of a
parallelogram.
Deriving Area Formulas
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Section 10.3, Slide 8
3
3
Find the perimeter of the parallelogram
Find the area of the parallelogram.
2
Any given
triangle can be
copied, rotated,
and joined.
They will form a
parallelogram.
Knowing the
area of a
parallelogram,
we get the area
of a triangle.
Deriving Area Formulas
© 2010 Pearson Education, Inc. All rights reserved.
Section 10.3, Slide 11
4
3
5
Find the perimeter of the triangle.
Find the area of the triangle.
2
We now know how to find the area of a
triangle.
Recall that every (convex) polygon can be
split up into triangles. That means we can
find their areas too!
1
2
1
2
Can you find the area of a triangle without
knowing the height? Yes!
a
b
c
Let s be the semi-perimeter (half the
perimeter), then...
Any trapezoid is
just two
triangles.
The heights are
the same, but
the bases are
different.
Base 1
h
Base 2
Deriving Area Formulas
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Section 10.3, Slide 17
Another way to get the
same formula.
2 copies of the same
trapezoid make a
parallelogram.
h
Base 1
+
Base 2
The area of one trapezoid is ½ the area
of the parallelogram.
Thus Area = ½ (b1 + b2) h
4
4
3
2
5
Find the perimeter of the trapezoid.
Find the area of the trapezoid.
The Pythagorean Theorem
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Section 10.3, Slide 20
The Pythagorean Theorem
• Example: Use the lengths of the
two given sides to find the length of
the third side in the given triangle.
The Pythagorean Theorem
• Example: Use the lengths of the
two given sides to find the length of
the third side in the given triangle.
• Solution:
Given:
and
Pythagorean Theorem:
© 2010 Pearson Education, Inc. All rights reserved.
Section 10.3, Slide 22
The Pythagorean Theorem
• Example: Find the length of
the third side in the given
triangle.
The Pythagorean Theorem
• Example: Find the length of
the third side in the given
triangle.
• Solution:
Given:
and
Pythagorean Theorem:
© 2010 Pearson Education, Inc. All rights reserved.
Section 10.3, Slide 24
The Pythagorean Theorem
• Example: The Great
Pyramid in Egypt has a
square base measuring
230 meters on each side,
and the distance from one
corner of the base to the
tip of the pyramid is 219
meters. What is the height
of the pyramid?
(continued on next slide)
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Section 10.3, Slide 25
The Pythagorean Theorem
• Solution:
Distance to center of base:
2
2
2
x =115 115 =13,22513,225=26450
x= 26,450≈162.6
Height of pyramid:
2
2
h 162.6 =219
2
2
h 26450=47,961
2
h =21,511
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Section 10.3, Slide 26
Circle
The number π, which appears in these formulas, is
the Greek letter pi. We will use 3.14 to approximate
pi.
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Section 10.3, Slide 27
How the Greeks found that the same π
turns up in both formulas:
A split up circle looks a lot like a
rectangle/parallelogram.
Circles
• Example: A man is designing a basketball
court in the form of a segment of a circle. There
will be a fence at the
rounded end of the
court, and he will paint
the court with a concrete
sealer. How much
fencing is required?
Hint: 1/6th of a circle.
© 2010 Pearson Education, Inc. All rights reserved.
(continued on next slide)
Section 10.3, Slide 29
Circles
• Solution:
The court is one-sixth of the interior of a circle
with a radius of 20 feet.
Circumference of full circle:
One-sixth of the circumference: 20.93 feet
© 2010 Pearson Education, Inc. All rights reserved.
Section 10.3, Slide 31