Holt CA Course 1

9-2Perimeter and Area of Triangles and Trapezoids

Warm Up

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Holt CA Course 1

9-2Perimeter and Area of Triangles and Trapezoids

Warm Up

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

2. Find the area.

1. Find the perimeter.64 ft

240 ft2

Holt CA Course 1

9-2Perimeter and Area of Triangles and Trapezoids

MG2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders.

Also covered: MG3.2

California

Standards

Holt CA Course 1

9-2Perimeter and Area of Triangles and Trapezoids

Additional Example 1: Using Perimeter

71 = 55 + d

d = 16 in.

P = 22 + 15 + 18 + d

16 = d

Substitute 71 for P.

Find the missing measurement when the perimeter is 71 in.

18 in.

22 in.

15 in.

Subtract 55 from both sides.

55 55

d

Holt CA Course 1

9-2Perimeter and Area of Triangles and Trapezoids

Check It Out! Example 1

58 = 49 + d

d = 9 in.

P = 28 + 7 + 14 + d

9 = d

Substitute 58 for P.

Find the missing measurement when the perimeter is 58 in.

14 in.

28 in.

7 in.

Subtract 49 from both sides.

49 49

d

Holt CA Course 1

9-2Perimeter and Area of Triangles and TrapezoidsAdditional Example 2: Multi-Step Application

Step 1: Find the length of the third side.

Substitute 12 for a and 20 for c.

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?

b = 16

a2 + b2 = c2

122 + b2 = 202

144 + b2 = 400b2 = 256

Use the Pythagorean Theorem.

√256 = 16.

Holt CA Course 1

9-2Perimeter and Area of Triangles and Trapezoids

Additional Example 3 Continued

Step 2: Find the perimeter of the yard.

Add all sides.

P = a + b + c

= 12 + 20 + 16

= 48

The border will be 48 feet long.

Holt CA Course 1

9-2Perimeter and Area of Triangles and Trapezoids

Check It Out! Example 2

Step 1: Find the length of the third side.

Substitute 38 for a and 32 for b.

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?

c ≈ 49.68

a2 + b2 = c2

382 + 322 = c2

1444 + 1024 = c2

2468 = c2

Use the Pythagorean Theorem.

√2468 49.68.

Holt CA Course 1

9-2Perimeter and Area of Triangles and Trapezoids

Check It Out! Example 2 Continued

Step 2: Find the perimeter of the yard.

Add all sides.

P = a + b + c

38 + 32 + 49.68

119.68

The border will be about 119.68 feet long.

Holt CA Course 1

9-2Perimeter and Area of Triangles and Trapezoids

A triangle or trapezoid can be thought of as half of a parallelogram. Therefore, the formulas for the

area of a triangle or trapezoid have as a factor.1 2

Holt CA Course 1

9-2Perimeter and Area of Triangles and Trapezoids

Holt CA Course 1

9-2Perimeter and Area of Triangles and Trapezoids

A. (–2, 2), (4, 2), (0, 5)

x

y

6

3

= 9 units2

A = bh12

Additional Example 3: Finding the 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.

Holt CA Course 1

9-2Perimeter and Area of Triangles and Trapezoids

B. (–1, 1), (4, 1), (4, 4), (0, 4)

= 13.5 units2

A = h(b1 + b2)12

= • 3(5 + 4)12

Area of a trapezoid

Substitute for h, b1, and b2.(–1, 1)

(0, 4) (4, 4)

x

y

(4, 1)

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

Additional Example 3: Finding the Area of Triangles and Trapezoids

5

3

4

Holt CA Course 1

9-2Perimeter and Area of Triangles and Trapezoids

A. (–1, –2), (5, –2), (5, 2), (–1, 6)

Check It Out! Example 3Graph 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

Holt CA Course 1

9-2Perimeter and Area of Triangles and Trapezoids

B. (–1, 1), (5, 1), (1, 5)

x

y

6

4

= 12 units2

A = bh12

Check It Out! Example 3

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

(5, 1)

(1, 5)

(–1, 1)= • 6 • 41

2

Area of a triangle

Substitute for b and h.

Holt CA Course 1

9-2Perimeter and Area of Triangles and Trapezoids

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