8-2 Perimeter and Area of Triangles and Trapezoids

Course 3

Warm Up

Problem of the Day

Lesson Presentation

Warm Up

Course 3

8-2 Perimeter and Area of Triangles and Trapezoids

A rectangle has sides lengths of 12 ft and 20 ft.

2. Find the area.

1. Find the perimeter.64 ft

240 ft2

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

8-2 Perimeter and Area of Triangles and Trapezoids

Learn to find the perimeter and area of triangles and trapezoids.

Perimeter and Area of Triangles and Trapezoids

Course 3

8-2 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

8-2 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

8-2 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

8-2 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

Check It Out: Example 1

Course 3

8-2 Perimeter and Area of Triangles and Trapezoids

Find the perimeter of each figure.

Additional Example 2: Finding a Missing Measurement

71 = 55 + d

d = 16 in.

P = 22 + 15 + 18 + d

16 = d

Substitute 71 for P.

Course 3

8-2 Perimeter and Area of Triangles and Trapezoids

Find the missing measurement for the trapezoid with perimeter 71 in.

18 in.

22 in.

15 in.

Subtract 55 from both sides.

55 = 55

d

Check It Out: Example 2

58 = 49 + d

d = 9 in.

P = 28 + 7 + 14 + d

9 = d

Substitute 58 for P.

Course 3

8-2 Perimeter and Area of Triangles and Trapezoids

Find the missing measurement for the trapezoid with perimeter 58 in.

14 in.

28 in.

7 in.

Subtract 49 from both sides.

49 = 49

d

Additional Example 3: Multi-Step Application

Find the length of the third side of the triangle using the Pythagorean Theorem.

Substitute 12 for a and 20 for c.

Course 3

8-2 Perimeter and Area of Triangles and Trapezoids

A homeowner wants to plant a border of shrubs around her yard that is in the shape of a right triangle. She knows that the length of the shortest side of the yard is 12 feet and the length of the longest side is 20 feet. How long will the border be?

√256 = 16.b = 16

a2 + b2 = c2

122 + b2 = 202

144 + b2 = 400b2 = 256

Additional Example 3 Continued

Find the perimeter of the yard.

Add all sides.

Course 3

8-2 Perimeter and Area of Triangles and Trapezoids

P = a + b + c

= 12 + 20 + 16

= 48

The border will be 48 feet long.

Check It Out: Example 3

Find the length of the third side of the triangle using the Pythagorean Theorem.

Substitute 38 for a and 32 for b.

Course 3

8-2 Perimeter and Area of Triangles and Trapezoids

A gardener wants to plant a border of flowers around the building that is in the shape of a right triangle. He knows that the length of the shortest sides of the building are 38 feet and 32 feet. How long will the border be?

√2468 = 49.68.c ≈ 49.68

a2 + b2 = c2

382 + 322 = c2

1444 + 1024 = c2

2468 = c2

Check It Out: Example 3 Continued

Find the perimeter of the yard.

Add all sides.

Course 3

8-2 Perimeter and Area of Triangles and Trapezoids

P = a + b + c

= 38 + 32 + 49.68

= 119.68

The border will be 119.68 feet long.

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

Course 3

8-2 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

8-2 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

8-2 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

(–2, 2), (4, 2), (0, 5)

x

y

6

3

= 9 units2

A = bh12

Additional Example 4: Finding the Area of Triangles and Trapezoids

Course 3

8-2 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.

(–1, –2), (5, –2), (5, 2), (–1, 6)

Check It Out: Example 4

Course 3

8-2 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

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

8-2 Perimeter and Area of Triangles and Trapezoids