6-2 Warm Up Problem of the Day Lesson Presentation Perimeter and Area of Triangles and Trapezoids 6-2 Warm Up Problem of the Day Lesson Presentation Pre-Algebra

Pre-Algebra 6-2 Perimeter and Area of Triangles and Trapezoids Warm Up 1. Find the perimeter of a rectangle with side lengths 12 ft and 20 ft. 64 ft 2. Find the area of a rectangle with side lengths 24 in. and 32 in. 768 in2 3. Find the area of a parallelogram with height 9 in. and base length 15 in. 135 in2

Problem of the Day The 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° 12 in2

Learning Goal Assignment Learn to find the area of triangles and trapezoids.

The figures show a fractal called the Koch snowflake 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.

Additional Example 1: Finding the Perimeter of Triangles and Trapezoids Find the perimeter of each figure. A. 7 Add all sides. 4 P = 4 + 7 + 10 10 = 21 units 17 8 11 6 Add all sides. B. P = 8 + 11 + 6 + 17 = 42 units

Try This: Example 1 Find the perimeter of each figure. Add all sides. 9 6 A. P = 9 + 6 + 11 = 26 units 11 22 Add all sides. B. 6 P = 6 + 22 + 5 + 16 5 = 49 units 16

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

AREA OF A TRIANGLE Words Numbers Formula Triangle: The area A of a triangle is one-half the base length b times the height h. A = (8)(4) = 16 units2 1 2

AREA OF A TRAPEZOID Words 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 = (h)(b1 + b2) 1 2 A = (2)(3 + 7) = 10 units2 1 2

Additional Example 2A: Finding the Area of Triangles and Trapezoids Graph and find the area of the figure with the given vertices. A. (–2, 2), (4, 2), (0, 5) Area of a triangle y A = bh 1 2 (0, 5) Substitute for b and h. = • 6 • 3 1 2 3 (–2, 2) (4, 2) 6 = 9 units2 x

Graph and find the area of the figure with the given vertices. Try This: Example 2A Graph and find the area of the figure with the given vertices. A. (–1, 1), (1, 7), (7, 1) Area of a triangle y (1, 7) A = bh 1 2 Substitute for b and h. 6 = • 8 • 6 1 2 (7, 1) (–1, 1) = 24 units2 x 8

Additional Example 2B: Finding the Area of Triangles and Trapezoids Graph and find the area of the figure with the given vertices. B. (–1, 2), (5, –2), (5, 2), (–1, 6) y (–1, 6) Area of a trapezoid A = h(b1 + b2) 1 2 (5, 2) Substitute for h, b1, and b2. 8 6 4 x = • 6(8 + 4) 1 2 (–1, –2) (5, –2) = 36 units2

Graph and find the area of the figure with the given vertices. Try This: Example 2B Graph and find the area of the figure with the given vertices. B. (–2, –1), (0, 5), (3, 5), (5, –1) y Area of a trapezoid 3 7 6 (3, 5) (0, 5) A = h(b1 + b2) 1 2 Substitute for h, b1, and b2. x = • 6(7 + 3) 1 2 (–2, –1) (5, –1) = 30 units2

Lesson Quiz Use the figure to find the following measurements. 1. The perimeter of the triangle 36 cm 2. The perimeter of the trapezoid 44 cm 3. The perimeter of the combined figure 64 cm 4. The area of the triangle 54 cm2 5. The area of the trapezoid 104 cm2