1. find the perimeter of a rectangle with side lengths 12 ft and 20 ft. 3. find the area of a...

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

Warm Up

Pre-Algebra

6.2

Perimeter and Area of Triangles and Trapezoids

Learn to find the 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.

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.

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.

Find the perimeter of each figure.

Example: Finding the Perimeter of Triangles and Trapezoids

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

Find the perimeter of each figure.

Try This

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

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

AREA OF A TRIANGLEAREA OF A TRIANGLEWords Numbers Formula

A = (8)(4)

= 16 units2

1 2

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

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.

Example: Finding the Area of Triangles and Trapezoids

B. (–1, 2), (5, –2), (5, 2), (–1, 6)

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

Example: Finding the Area of Triangles and Trapezoids

A. (–1, 1), (1, 7), (7, 1)

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

Try This

B. (–2, –1), (0, 5), (3, 5), (5, –1)

(–2, –1)

(0, 5) (3, 5)

x

y

(5, –1)

3

7

6

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.

Try This

Use 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

Lesson Quiz