Perimeter & Area
MATH 102
Contemporary Math
S. Rook
Overview
• Section 10.3 in the textbook:
– Perimeter & area
– Pythagorean theorem
Perimeter & Area
Perimeter & Area in General
• Perimeter: the sum of the lengths of the sides
of a polygon
– i.e. the length around (“rim”) the polygon
– Measured using the same units as the sides
• Area: the amount of space inside of the
polygon
– Measured in square units of the sides
• On the next few slides are formulas for
perimeter and area for common polygons
Parallelogram
• Recall the shape and characteristics of a
parallelogram
• No special formula for perimeter
– Just add the lengths of all the sides
• For a parallelogram with height h and base b,
area = h x b
– The height is a straight vertical line
– See page 471 for theory
Trapezoid
• Recall the shape and characteristics of a
trapezoid
• No special formula for perimeter
– Just add up the sides
• For a trapezoid with lower base b1, upper base
b2, and height h, area = ½ (b1 + b2) x h
– b1 and b2 are parallel to each other
– The height h is a straight vertical line
Triangle
• No special formula for perimeter
– Just add up the lengths of all the sides
• For a triangle with a height h and a base b,
area = ½ b x h
– The height h is a straight vertical line
Rectangle & Square
• Recall that a rectangle has two pairs of
corresponding sides each equal in length
• Given a rectangle with length l and width w:
– Perimeter = 2l + 2w
– Area = l x w
• Recall that a square is a rectangle, but with four
equal sides
– i.e. l and w are the same length
• Given a square with a sides of length l:
– Perimeter = 4l
– Area = l2
Circle
• Recall that the line segment with endpoints at
the center of the circle and on the outside of
the circle is known as the radius
• Given a circle with radius r:
– Circumference = 2πr
• Circumference is the circle’s equivalent to perimeter
– Area = πr2
π (pi) is a special constant in mathematics related
to the circumference of a circle and its diameter
• π is infinite so we often approximate it as 3.14
Perimeter & Area (Example)
Ex 1: Susan wishes to plant Black-Eyed Susans in
her circular garden which has a radius of 5
feet. If a package of seeds will cover 12
square feet of her garden, how many whole
packages of seeds must Susan buy in order to
cover the entire garden?
Perimeter & Area (Example)
Ex 2: The owners of a 50 foot by 20 foot
rectangular field have decided to install a
walkway which will border the field. If the
walkway extends 5 feet in all directions, find
the perimeter of the walkway.
Perimeter & Area (Example)
Ex 3: Find the area of the shaded region:
a)
b)
Pythagorean Theorem
Pythagorean Theorem
• Pythagorean Theorem: given a right triangle with
legs a & b and hypotenuse c, the following
relationship exists: a2 + b2 = c2
– It does not matter which
the legs is a and which
– The hypotenuse, c, is the longest
side AND is ALWAYS opposite the
90°-angle
of
is b
• When solving problems with right triangles, it is
often helpful to draw a picture
14
Pythagorean Theorem (Example)
Ex 4: A 25-foot ladder leans on the roof of a 20
foot-tall building. How far from the building
does the base of the ladder extend?
Pythagorean Theorem (Example)
Ex 5: Find the area of the parallelogram:
Summary
• After studying these slides, you should know
how to do the following:
– Solve problems involving area & perimeter of
common polygons and circles
– Understand and apply the Pythagorean Theorem
• Additional Practice:
– See problems in Section 10.3
• Next Lesson:
– Volume & Surface Area (Section 10.4)