9-4 Area of Triangles and Trapezoids

Course 2

Warm UpWarm UpProblem of the DayProblem of the DayLesson PresentationLesson Presentation

Warm UpEvaluate.

2419.4468

Course 2

9-4 Area of Triangles and Trapezoids

12 · 6 · 812 · 5.4 · 7.2

3. 4(7 + 10)4. 3.5(12 + 8.2)

1.

70.7

2.

Problem of the Day

(5.5)(1.5) = 8.25 in2

Course 2

9-4 Area of Triangles and Trapezoids

4 in.1.5 in.

7 in.

An isosceles trapezoid has bases of 7 in. and 4 in. and height 1.5 in. Find its area by using only the formula for the area of a parallelogram.

Learn to find the area of triangles and trapezoids.

Area of Triangles and Trapezoids

Course 2

9-4 Area of Triangles and Trapezoids

Course 2

9-4 Area of Triangles and Trapezoids

AREA OF A TRIANGLE

h

b

A = 12

bhThe area A of a triangleis half the product of itsbase b and its height h.

Find the area of the triangle.

Additional Example 1A: Finding the Area of a Triangle

Course 2

9-4 Area of Triangles and Trapezoids

5

8

A = 12 bh Use the formula.

A = 12 (8 · 5) Substitute 8 for b and 5 for h.

A = 20

The area of the triangle is 20 square units.

Find the area of the triangle.

Additional Example 1B: Finding the Area of a Triangle

Course 2

9-4 Area of Triangles and Trapezoids

9

A = 12bh Use the formula.

A = 12 (9 · 12) Substitute 9 for b and 12 for h.

A = 54

The area of the triangle is 54 square units.

12

Find the area of the triangle.

Course 2

9-4 Area of Triangles and Trapezoids

A = 12 bh Use the formula.

A = 12 (6 · 9) Substitute 6 for b and 9 for h.

A = 27

The area of the triangle is 27 square units.

Check It Out: Example 1A

6

9

Find the area of the triangle.

Course 2

9-4 Area of Triangles and Trapezoids

A = 12 bh Use the formula.

A = 12 (7 · 10) Substitute 7 for b and 10 for h.

A = 35

The area of the triangle is 35 square units.

Check It Out: Example 1B

10

7

Course 2

9-4 Area of Triangles and Trapezoids

The two parallel sides of a trapezoid are its bases, b1 and b2. The height of a trapezoid is the perpendicular distance between the bases.

h

b1

b2

Course 2

9-4 Area of Triangles and Trapezoids

AREA OF A TRAPEZOID

h

b1

A = 12h(b1 + b2)

The area of a trapezoid is half its height multiplied by the sum of its two bases.

b2

In the term b1, the number 1 is called a subscript. It is read as “b-one” or “b sub-one.”

Reading Math

Find the area of the trapezoid.

Additional Example 2A: Finding the Area of a Trapezoid

Course 2

9-4 Area of Triangles and Trapezoids

5 in.

6 in.

9 in.

A = 12

h(b1 + b2) Use the formula.A = 1

2· 6(5 + 9)

A =12 · 6(14)

A = 42

The area of the trapezoid is 42 in2.

Substitute.

Multiply.

Add.

Find the area of the trapezoid.

Additional Example 2B: Finding the Area of a Trapezoid

Course 2

9-4 Area of Triangles and Trapezoids

A = 12

h(b1 + b2) Use the formula.A = 1

2· 7(12 + 16)

A =12 · 7(28)

A = 98

The area of the trapezoid is 98 cm2.

Substitute.

Multiply.

Add.

12 cm

16 cm

7 cm

Find the area of the trapezoid.

Course 2

9-4 Area of Triangles and Trapezoids

A = 12

h(b1 + b2) Use the formula.A = 1

2· 6(11 + 4)

A =12 · 6(15)

A = 45

The area of the trapezoid is 45 in2.

Substitute.

Multiply.

Add.

Check It Out: Example 2A

4 in.6 in.11 in.

Find the area of the trapezoid.

Course 2

9-4 Area of Triangles and Trapezoids

A = 12

h(b1 + b2) Use the formula.A = 1

2· 9(5 + 16)

A =12 · 9(21)

A = 94.5

The area of the trapezoid is 94.5 cm2.

Substitute.

Multiply.

Add.

Check It Out: Example 2B

16 cm

5 cm9 cm

The state of Wisconsin is shaped somewhat like a trapezoid. What is the approximate area of the state?

Additional Example 3: Geometry Application

Course 2

9-4 Area of Triangles and Trapezoids

A = 12

h(b1 + b2) Use the formula.

A = 12

· 300(153 + 220)

A =12 · 300(373)

A = 55,950

The area of Wisconsin is approximately 56,000 square miles.

Substitute.

Multiply.

Add.

A large preserve has a similar trapezoid shape. What is the approximate area of the preserve?

Check It Out: Example 3

Course 2

9-4 Area of Triangles and Trapezoids

232 mi

116 mi

A = 12

h(b1 + b2) Use the formula.

A = 12

· 129(232 + 116)

A =12 · 129(347)

A = 22,446

The area of the preserve is approximately 22,446 square miles.

Substitute.

Multiply.

Add.

129 mi

Lesson QuizFind the area of each figure.

1.

3.

9 in245 ft2

Insert Lesson Title Here

60 ft2 87.5 ft2

Course 2

9-4 Area of Triangles and Trapezoids

2.

4.

4. What is the height of a triangle with area 36 cm2 and a base 9 cm? 8 cm