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This pdf briefly explains finding the area of triangles and trapezoids. The area A of a triangle is half the product of its base b and its height h. A parallelogram can be divided into two congruent trapezoids. The area of each trapezoid is one-half the area of the parallelogram.

1.
Areaof

8-5 Area ofTriangles

Trianglesand

andTrapezoids

Trapezoids

Learn to find the area of triangles and

trapezoids.

Course 2

8-5 Area ofTriangles

Trianglesand

andTrapezoids

Trapezoids

Learn to find the area of triangles and

trapezoids.

Course 2

2.
8-5 Area of Triangles and Trapezoids

A diagonal of a parallelogram divides the

parallelogram into two congruent triangles. So the

area of each triangle is half the area of the

parallelogram.

Height

Height

Base Base

The base of a triangle can be any side. The height of

a triangle is the perpendicular distance from the

base to the opposite vertex.

Course 2

A diagonal of a parallelogram divides the

parallelogram into two congruent triangles. So the

area of each triangle is half the area of the

parallelogram.

Height

Height

Base Base

The base of a triangle can be any side. The height of

a triangle is the perpendicular distance from the

base to the opposite vertex.

Course 2

3.
8-5 Area of Triangles and Trapezoids

AREA OF A TRIANGLE

The area A of a triangle

is half the product of its A = 1 bh h

2

base b and its height h.

b

Course 2

AREA OF A TRIANGLE

The area A of a triangle

is half the product of its A = 1 bh h

2

base b and its height h.

b

Course 2

4.
8-5 Areas of Triangles and Trapezoids

Additional Example 1A: Finding the Area of a

Triangle

Find the area of the triangle.

A.

A = 1 bh Use the formula.

2

5

A = 1 (8 · 5) Substitute 8 for b and

8 2 5 for h.

A = 20

The area of the triangle is 20 square units.

Course 2

Additional Example 1A: Finding the Area of a

Triangle

Find the area of the triangle.

A.

A = 1 bh Use the formula.

2

5

A = 1 (8 · 5) Substitute 8 for b and

8 2 5 for h.

A = 20

The area of the triangle is 20 square units.

Course 2

5.
8-5 Area of Triangles and Trapezoids

Additional Example 1B: Finding the area of a

Triangle

Find the area of the triangle.

B.

A = 1 bh Use the formula.

2

12

A =1 (9 · 12) Substitute 9 for b and

2 12 for h.

9

A = 54

The area of the triangle is 54

square units.

Course 2

Additional Example 1B: Finding the area of a

Triangle

Find the area of the triangle.

B.

A = 1 bh Use the formula.

2

12

A =1 (9 · 12) Substitute 9 for b and

2 12 for h.

9

A = 54

The area of the triangle is 54

square units.

Course 2

6.
8-5 Areas of Triangles and Trapezoids

Try This: Example 1A

Find the area of the triangle.

A.

A = 1 bh Use the formula.

2

9 A = 1 (6 · 9) Substitute 6 for b and

2 9 for h.

6 A = 27

The area of the triangle is 27 square units.

Course 2

Try This: Example 1A

Find the area of the triangle.

A.

A = 1 bh Use the formula.

2

9 A = 1 (6 · 9) Substitute 6 for b and

2 9 for h.

6 A = 27

The area of the triangle is 27 square units.

Course 2

7.
8-5 Areas of Triangles and Trapezoids

Try This: Example 1B

Find the area of the triangle.

B.

A = 1 bh Use the formula.

2

10 A = 1 (7 · 10) Substitute 7 for b and

2 10 for h.

A = 35

7

The area of the triangle is 35 square units.

Course 2

Try This: Example 1B

Find the area of the triangle.

B.

A = 1 bh Use the formula.

2

10 A = 1 (7 · 10) Substitute 7 for b and

2 10 for h.

A = 35

7

The area of the triangle is 35 square units.

Course 2

8.
8-5 Area of Triangles and Trapezoids

A parallelogram can be divided into two

congruent trapezoids. The area of each trapezoid

is one-half the area of the parallelogram.

Area of a trapezoid = 1 (base of

2

parallelogram)(height).

Course 2

A parallelogram can be divided into two

congruent trapezoids. The area of each trapezoid

is one-half the area of the parallelogram.

Area of a trapezoid = 1 (base of

2

parallelogram)(height).

Course 2

9.
8-5 Area of Triangles and Trapezoids

The two parallel sides of a trapezoid are its bases.

If we call the longer side b1 and the shorter side

b2, then the base of the parallelogram is b1 + b2.

Area of a trapezoid = 1 (base 1 +

2

base 2)(height).

Course 2

The two parallel sides of a trapezoid are its bases.

If we call the longer side b1 and the shorter side

b2, then the base of the parallelogram is b1 + b2.

Area of a trapezoid = 1 (base 1 +

2

base 2)(height).

Course 2

10.
8-5 Area of Triangles and Trapezoids

AREA OF A TRAPEZOID

The area of a trapezoid b2

is half its height A = 1 h(b1 + b2)

multiplied by the sum of 2 h

its two bases. b1

Course 2

AREA OF A TRAPEZOID

The area of a trapezoid b2

is half its height A = 1 h(b1 + b2)

multiplied by the sum of 2 h

its two bases. b1

Course 2

11.
8-5 Areas of Triangles and Trapezoids

Additional Example 2A: Finding the Area of a

Trapezoid

Find the area of the trapezoid.

A. 5 in. A = 1 h(b1 + b2) Use the formula.

2

6 in. A = 1 · 6(5 + 9) Substitute.

2

A = 1 · 6(14) Add.

9 in. 2

A = 42 Multiply.

The area of the trapezoid is 42 in2.

Course 2

Additional Example 2A: Finding the Area of a

Trapezoid

Find the area of the trapezoid.

A. 5 in. A = 1 h(b1 + b2) Use the formula.

2

6 in. A = 1 · 6(5 + 9) Substitute.

2

A = 1 · 6(14) Add.

9 in. 2

A = 42 Multiply.

The area of the trapezoid is 42 in2.

Course 2

12.
8-5 Areas of Triangles and Trapezoids

Additional Example 2B: Finding the Area of a

Trapezoid

Find the area of the trapezoid.

B.

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

2

7 cm A = 1 · 7(12 + 16) Substitute.

2

16 cm A = 1 · 7(28) Add.

2

A = 98 Multiply.

The area of the trapezoid is 98 cm2.

Course 2

Additional Example 2B: Finding the Area of a

Trapezoid

Find the area of the trapezoid.

B.

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

2

7 cm A = 1 · 7(12 + 16) Substitute.

2

16 cm A = 1 · 7(28) Add.

2

A = 98 Multiply.

The area of the trapezoid is 98 cm2.

Course 2

13.
8-5 Areas of Triangles and Trapezoids

Try This: Example 2A

Find the area of the trapezoid.

A.

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

2

A = 1 · 6(11 + 4) Substitute.

11 in. 4 in. 2

6 in.

A = 1 · 6(15) Add.

2

A = 45 Multiply.

The area of the trapezoid is 45 in2.

Course 2

Try This: Example 2A

Find the area of the trapezoid.

A.

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

2

A = 1 · 6(11 + 4) Substitute.

11 in. 4 in. 2

6 in.

A = 1 · 6(15) Add.

2

A = 45 Multiply.

The area of the trapezoid is 45 in2.

Course 2

14.
8-5 Areas of Triangles and Trapezoids

Try This: Example 2B

Find the area of the trapezoid.

B.

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

16 cm 2

A = 1 · 9(5 + 16) Substitute.

9 cm 2

5 cm A = 1 · 9(21) Add.

2

A = 94.5 Multiply.

The area of the trapezoid is 94.5 cm2.

Course 2

Try This: Example 2B

Find the area of the trapezoid.

B.

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

16 cm 2

A = 1 · 9(5 + 16) Substitute.

9 cm 2

5 cm A = 1 · 9(21) Add.

2

A = 94.5 Multiply.

The area of the trapezoid is 94.5 cm2.

Course 2

15.
8-5 Area

Insert

ofLesson

Triangles

Title

and

Here

Trapezoids

Lesson Quiz

Find the area of each figure.

1. 2. 9 in2

45 ft2 3 in.

9 ft

10 ft 6 in.

8 ft 10 ft

3. 4. 87.5 ft2

6 ft 60 ft2 7 ft

12 ft 15 ft

5. What is the height of a triangle with area

36 cm2 and a base 9 cm? 8 cm

Course 2

Insert

ofLesson

Triangles

Title

and

Here

Trapezoids

Lesson Quiz

Find the area of each figure.

1. 2. 9 in2

45 ft2 3 in.

9 ft

10 ft 6 in.

8 ft 10 ft

3. 4. 87.5 ft2

6 ft 60 ft2 7 ft

12 ft 15 ft

5. What is the height of a triangle with area

36 cm2 and a base 9 cm? 8 cm

Course 2

16.
Homework

8-5 Worksheet

Study for fraction quiz Thursday

8-5 Worksheet

Study for fraction quiz Thursday