Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Warm Up A rectangle has sides lengths of 12 ft and 20 ft. 1. Find the perimeter. 64 ft 2. Find the area. 240 ft2

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.) 12 in2 60°

Learn to find the perimeter and 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

Check It Out: 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

Additional Example 2: Finding a Missing Measurement Find the missing measurement for the trapezoid with perimeter 71 in. 18 in. 15 in. d 22 in. P = 22 + 15 + 18 + d 71 = 55 + d Substitute 71 for P. –55 = –55 Subtract 55 from both sides. 16 = d d = 16 in.

Check It Out: Example 2 Find the missing measurement for the trapezoid with perimeter 58 in. 14 in. 7 in. d 28 in. P = 28 + 7 + 14 + d 58 = 49 + d Substitute 58 for P. –49 = –49 Subtract 49 from both sides. 9 = d d = 9 in.

Additional Example 3: Multi-Step Application 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? Find the length of the third side of the triangle using the Pythagorean Theorem. a2 + b2 = c2 122 + b2 = 202 Substitute 12 for a and 20 for c. 144 + b2 = 400 b2 = 256 b = 16 √256 = 16.

Additional Example 3 Continued Find the perimeter of the yard. P = a + b + c = 12 + 20 + 16 Add all sides. = 48 The border will be 48 feet long.

Check It Out: Example 3 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? Find the length of the third side of the triangle using the Pythagorean Theorem. a2 + b2 = c2 382 + 322 = c2 Substitute 38 for a and 32 for b. 1444 + 1024 = c2 2468 = c2 c ≈ 49.68 √2468 = 49.68.

Check It Out: Example 3 Continued Find the perimeter of the yard. P = a + b + c = 38 + 32 + 49.68 Add all sides. = 119.68 The border will be about 119.68 feet long.

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

Additional Example 4: Finding the Area of Triangles and Trapezoids Graph and find the area of the figure with the given vertices. (–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. Check It Out: Example 4 Graph and find the area of the figure with the given vertices. (–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

Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 19

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

Lesson Quiz for Student Response Systems 1. Find the perimeter of the triangle. A. 15 cm B. 14 cm C. 13 cm D. 12 cm 21

Lesson Quiz for Student Response Systems 2. Find the perimeter of the trapezoid. A. 21 in. B. 31 in. C. 51 in. D. 61 in. 22

Lesson Quiz for Student Response Systems 3. Find the perimeter of the combined figure. A. 14 in. B. 17 in. C. 20 in. D. 21 in. 23

Lesson Quiz for Student Response Systems 4. Find the perimeter of the combined figure. A. 100 ft2 B. 1407 ft2 C. 200 ft2 D. 260 ft2 24