Course 3 Chapter 6 Lesson 2

1
Perimeter and Area of
Triangles and Trapezoids
6-2
Warm Up
Problem of the Day
Lesson Presentation
Course 3
2
Warm Up
1. Find the perimeter of a rectangle with side
lengths 12 ft and 20 ft.
64 ft
2. Find the area of a rectangle with side
lengths 24 in. and 32 in.
768 in2
3. Find the area of a parallelogram with height
9 in. and base length 15 in.
135 in2
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 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
Try This 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
A triangle or trapezoid can be thought of as half
of a parallelogram.
10
Triangle The area A of a triangle is one-half
the base length b times the height h.
11
Trapezoid The area of a trapezoid is one-half
the height h times the sum of the base lengths b1
and b2.
12
Additional Example 2A Finding the Area of
Triangles and Trapezoids
Graph and find the area of the figure with the
given vertices.
A. (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
13
Additional Example 2B Finding the Area of
Triangles and Trapezoids
Graph and find the area of the figure with the
given vertices.
B. (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
14
Try This Example 2A
Graph and find the area of the figure with the
given vertices.
A. (1, 1), (1, 7), (7, 1)
Area of a triangle
(1, 7)
Substitute for b and h.
6
(7, 1)
(1, 1)
24 units2
8
15
Try This Example 2B
Graph and find the area of the figure with the
given vertices.
B. (2, 1), (0, 5), (3, 5), (5, 1)
y
Area of a trapezoid
(3, 5)
(0, 5)
Substitute for h, b1, and b2.
x
(2, 1)
(5, 1)
30 units2
16
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