Course 3 Chapter 6 Lesson 2

1
Perimeter and Area of
Triangles and Trapezoids
8-2
Warm Up
Problem of the Day
Lesson Presentation
Course 3
2
Warm Up
A rectangle has sides lengths of 12 ft and 20 ft.
1. Find the perimeter.
64 ft
2. Find the area.
240 ft2
3
Problem of the Day The area of a rhombus with two
60 angles is 24 in2. An equilateral triangle is
drawn so that one side is a side of the rhombus.
What is the area of the triangle? (Hint You
don't have to use a formula.)
12 in2
4
Perimeter and Area of Triangles and Trapezoids
Learn to find the perimeter and area of triangles
and trapezoids.
5
The figures show a fractal called the Koch
snowflake. It is constructed by first drawing an
equilateral triangle. Then triangles with sides
one-third the length of the original sides are
added to the middle of each side. The second step
is then repeated over and over again.
6
The area and perimeter of each figure is larger
than that of the one before it. However, the area
of any figure is never greater than the area of
the box, while the perimeters increase without
bound. To find the area and perimeter of each
figure, you must be able to find the area of a
triangle.
7
Additional Example 1 Finding the Perimeter of
Triangles and Trapezoids
Find the perimeter of each figure.
7
A.
Add all sides.
4
P 4 7 10
10
21 units
Add all sides.
B.
P 8 11 6 17
42 units
8
Check It Out Example 1
Find the perimeter of each figure.
Add all sides.
6
9
P 9 6 11
A.
26 units
11
22
Add all sides.
B.
6
P 6 22 5 16
5
49 units
16
9
Additional Example 2 Finding a Missing
Measurement
Find the missing measurement for the trapezoid
with perimeter 71 in.
18 in.
15 in.
d
22 in.
P 22 15 18 d
71 55 d
Substitute 71 for P.
Subtract 55 from both sides.
-55 -55
16 d
d 16 in.
10
Check It Out Example 2
Find the missing measurement for the trapezoid
with perimeter 58 in.
14 in.
7 in.
d
28 in.
P 28 7 14 d
58 49 d
Substitute 58 for P.
Subtract 49 from both sides.
-49 -49
9 d
d 9 in.
11
Additional Example 3 Multi-Step Application
A homeowner wants to plant a border of shrubs
around her yard that is in the shape of a right
triangle. She knows that the length of the
shortest side of the yard is 12 feet and the
length of the longest side is 20 feet. How long
will the border be?
Find the length of the third side of the triangle
using the Pythagorean Theorem.
a2 b2 c2
Substitute 12 for a and 20 for c.
122 b2 202
144 b2 400
b2 256
v256 16.
b 16
12
Additional Example 3 Continued
Find the perimeter of the yard.
P a b c
12 20 16
Add all sides.
48
The border will be 48 feet long.
13
Check It Out Example 3
A gardener wants to plant a border of flowers
around the building that is in the shape of a
right triangle. He knows that the length of the
shortest sides of the building are 38 feet and 32
feet. How long will the border be?
Find the length of the third side of the triangle
using the Pythagorean Theorem.
a2 b2 c2
382 322 c2
Substitute 38 for a and 32 for b.
1444 1024 c2
2468 c2
v2468 49.68.
c 49.68
14
Check It Out Example 3 Continued
Find the perimeter of the yard.
P a b c
38 32 49.68
Add all sides.
119.68
The border will be 119.68 feet long.
15
A triangle or trapezoid can be thought of as half
of a parallelogram.
16
AREA OF A TRIANGLE AREA OF A TRIANGLE AREA OF A TRIANGLE
Words Numbers Formula

Triangle The area A of a triangle is one-half
the base length b times the height h.
17
AREA OF A TRAPEZOID AREA OF A TRAPEZOID AREA OF A TRAPEZOID
Words Numbers Formula

Trapezoid The area of a trapezoid is one-half
the height h times the sum of the base lengths
b1 and b2.
18
Additional Example 4 Finding the Area of
Triangles and Trapezoids
Graph and find the area of the figure with the
given vertices.
(2, 2), (4, 2), (0, 5)
Area of a triangle
(0, 5)
Substitute for b and h.
3
(2, 2)
(4, 2)
6
9 units2
19
Check It Out Example 4
Graph and find the area of the figure with the
given vertices.
(1, 2), (5, 2), (5, 2), (1, 6)
y
(1, 6)
Area of a trapezoid
(5, 2)
Substitute for h, b1, and b2.
4
8
x
6
(1, 2)
(5, 2)
36 units2
20
Lesson Quiz
Use the figure to find the following measurements.
1. The perimeter of the triangle
36 cm
2. The perimeter of the trapezoid
44 cm
64 cm
3. The perimeter of the combined figure
4. The area of the triangle
54 cm2
104 cm2
5. The area of the trapezoid