Warm UpEvaluate.

24

19.44

68

Course 2

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

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

Area of Triangles and Trapezoids

Area of Triangles and Trapezoids

Course 2

AF 3.1 Use variables in expressions describing geometric quantities.

-Objective :Students will use variables in expressions describing geometric quantities for Areas of triangles and trapezoids by using equation formulas and scoring an 80% proficiency on an exit slip.

Course 2

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.

Base

HeightHeight

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

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

Areas of Triangles and Trapezoids

A.

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

Area of Triangles and Trapezoids

B.

9

A = 12

bh 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

Areas of Triangles and Trapezoids

A. 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.

Try This: Example 1A

6

9

Find the area of the triangle.

Course 2

Areas of Triangles and Trapezoids

B. 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.

Try This: Example 1B

10

7

Course 2

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 = 12

(base of

parallelogram)(height).

Course 2

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 = 12

(base 1 +

base 2)(height).

Course 2

Area of Triangles and Trapezoids

AREA OF A TRAPEZOID

h

b1

A = 12

h(b1 + b2)

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

b2

Find the area of the trapezoid.

Additional Example 2A: Finding the Area of a Trapezoid

Course 2

Areas of Triangles and Trapezoids

A. 5 in.

6 in.

9 in.

A = 12

h(b1 + b2) Use the formula.

A = 12

· 6(5 + 9)

A =12

· 6(14)

A = 42

The area of the trapezoid is 42 in2.

Substitute.

Multiply.

Add.84

Find the area of the trapezoid.

Additional Example 2B: Finding the Area of a Trapezoid

Course 2

Areas of Triangles and Trapezoids

B. A = 1

2h(b1 + b2) Use the formula.

A = 12

· 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

196

Find the area of the trapezoid.

Course 2

Areas of Triangles and Trapezoids

A. A = 1

2h(b1 + b2) Use the formula.

A = 12

· 6(11 + 4)

A =12

· 6(15)

A = 45

The area of the trapezoid is 45 in2.

Substitute.

Multiply.

Add.

Try This: Example 2A

4 in.6 in.

11 in.

90

Find the area of the trapezoid.

Course 2

Areas of Triangles and Trapezoids

B. A = 1

2h(b1 + b2) Use the formula.

A = 12

· 9(5 + 16)

A =12

· 9(21)

A = 94.5

The area of the trapezoid is 94.5 cm2.

Substitute.

Multiply.

Add.

Try This: Example 2B

16 cm

5 cm

9 cm

189

Area of Triangles Exploration Activity

1) Cut out the pieces of the rectangle and the dotted rectangle and glue each piece on your notebook.2) Use the ruler to find the sides of the rectangle and triangles in inches.(Find the Length and Width of the Rectangles and the Base and Height of Each triangle)

3) Once you have all the measurements, find the AREA for each shape!

Use : A = L X W Use: (Base x Height)12

Lesson Exit Slip

Find the area of each figure.

1.

3.

9 in2

45 ft2

Insert Lesson Title Here

60 ft287.5 ft2

Course 2

Area of Triangles and Trapezoids

2.9 ft

10 ft

3 in.

6 in.

8 ft

12 ft

6 ft

10 ft

7 ft

15 ft

4.

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