6-2 perimeter and area of triangles and trapezoids course 3 warm up warm up problem of the day...

6-2 Perimeter and Area of Triangles and Trapezoids

Course 3

Warm Up

Problem of the Day

Lesson Presentation

Warm Up

Course 3

6-2 Perimeter and Area of Triangles and Trapezoids

1. Find the perimeter of a rectangle with side lengths 12 ft and 20 ft.

3. Find the area of a parallelogram with height 9 in. and base length 15 in.

2. Find the area of a rectangle with side lengths 24 in. and 32 in.

64 ft

768 in2

135 in2

Problem of the DayThe 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.)

60°

60°

12 in2

Course 3

6-2 Perimeter and Area of Triangles and Trapezoids

Learn to find the area of triangles and trapezoids.

Perimeter and Area of Triangles and Trapezoids

Course 3

6-2 Perimeter and Area of Triangles and Trapezoids

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.

Course 3

6-2 Perimeter and Area of Triangles and Trapezoids

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.

Course 3

6-2 Perimeter and Area of Triangles and Trapezoids

Additional Example 1: Finding the Perimeter of Triangles and Trapezoids

A. 4

10= 21 units

B.

= 42 units

7

17

811

6

P = 4 + 7 + 10

Add all sides.

P = 8 + 11 + 6 + 17

Add all sides.

Course 3

6-2 Perimeter and Area of Triangles and Trapezoids

Find the perimeter of each figure.

A.6

11

P = 9 + 6 + 11

Add all sides.9

= 26 units

B.

22

5 P = 6 + 22 + 5 + 16

= 49 units

Add all sides.

16

6

Try This: Example 1

Course 3

6-2 Perimeter and Area of Triangles and Trapezoids

Find the perimeter of each figure.

A triangle or trapezoid can be thought of as half of a parallelogram.

Course 3

6-2 Perimeter and Area of Triangles and Trapezoids

Triangle: The area A of a triangle is one-half the base length b times the height h.

Course 3

6-2 Perimeter and Area of Triangles and Trapezoids

AREA OF A TRIANGLEAREA OF A TRIANGLEWords Numbers Formula

A = (8)(4)

= 16 units2

1 2

Course 3

6-2 Perimeter and Area of Triangles and Trapezoids

AREA OF A TRAPEZOIDAREA OF A TRAPEZOIDWords Numbers Formula

Trapezoid: The area of a trapezoid is one-half the height h times the sum of the base lengths b1 and b2.

A = (2)(3 + 7)

= 10 units2

1 2

A = (h)(b1 + b2)

1 2

A. (–2, 2), (4, 2), (0, 5)

x

y

6

3

= 9 units2

A = bh12

Additional Example 2A: Finding the Area of Triangles and Trapezoids

Course 3

6-2 Perimeter and Area of Triangles and Trapezoids

Graph and find the area of the figure with the given vertices.

(4, 2)

(0, 5)

(–2, 2)= • 6 • 31

2

Area of a triangle

Substitute for b and h.

B. (–1, 2), (5, –2), (5, 2), (–1, 6)

Additional Example 2B: Finding the Area of Triangles and Trapezoids

Course 3

6-2 Perimeter and Area of Triangles and Trapezoids

Graph and find the area of the figure with the given vertices.

= 36 units2

A = h(b1 + b2)12

= • 6(8 + 4)12

Area of a trapezoid

Substitute for h, b1, and b2.

(–1, –2)

(–1, 6)

(5, 2)

x

y

(5, –2)

48 6

A. (–1, 1), (1, 7), (7, 1)

Try This: Example 2A

Course 3

6-2 Perimeter and Area of Triangles and Trapezoids

Graph and find the area of the figure with the given vertices.

x

y

8

(1, 7)

(–1, 1) (7, 1)= 24 units2

A = bh12

= • 8 • 612

Area of a triangle

Substitute for b and h.6

B. (–2, –1), (0, 5), (3, 5), (5, –1)

(–2, –1)

(0, 5) (3, 5)

x

y

(5, –1)

3

7

6

Try This: Example 2B

Course 3

6-2 Perimeter and Area of Triangles and Trapezoids

Graph and find the area of the figure with the given vertices.

= 30 units2

A = h(b1 + b2)12

= • 6(7 + 3)12

Area of a trapezoid

Substitute for h, b1, and b2.

Lesson QuizUse the figure to find the following measurements.

1. The perimeter of the triangle

2. The perimeter of the trapezoid

3. The perimeter of the combined figure

4. The area of the triangle

5. The area of the trapezoid

36 cm

44 cm

54 cm2

64 cm

104 cm2

Course 3

6-2 Perimeter and Area of Triangles and Trapezoids