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1.7 Introduction to Perimeter, Circumference, and Area GOAL 1 Find the perimeter and area of common plane figures. GOAL 2 Use a general problem-solving plan. What you should learn To solve real-life problems about perimeter and area, such as finding the number of bags of seed you need for a field. Why you should learn it

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GOAL 1 REVIEWING PERIMETER, CIRCUMFERENCE, AND AREA 1.7 Introduction to Perimeter, Circumference, and Area You are expected to know and be able to use the formulas for perimeter (P), area (A), and circumference (C) found on page 51 of the text. You should have these formulas memorized by the time you have completed the assignment. They are reviewed on the next slide.

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PERIMETER, CIRCUMFERENCE, AND AREA FORMULAS P = 4s SQUARE side length s s s s s s A = s 2 RECTANGLE length l and width w l w P = 2l + 2w ll w w A = lw TRIANGLE side lengths a, b, and c, base b, and height h ah b c P = a + b + c a b c CIRCLE radius r r

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EXAMPLE 1 You are expected to use the correct type of units for perimeter, circumference, and area. The units used for perimeter and circumference are units of ______, and the units used for area are ______ units. lengthsquare The expression cm 2 is read as square centimeters, m 2 is read square meters, and so on. Know how to read these and other units correctly!

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Extra Example 1 EXAMPLE 2 Find the perimeter and area of a rectangle of length 4.5 m and width 0.5 m. Hint: draw and label a sketch, then write the correct formulas. l = 4.5 m w = 0.5 m Click for the solutions

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Extra Example 2 EXAMPLE 3 A road sign consists of a pole with a circular sign on top. The top of the circle is 10 feet high and the bottom of the circle is 8 feet high. Find the diameter, radius, circumference, and area of the circle. Use 3.14 as an approximation for π, and round your answers to the nearest tenth. 10 ft 8 ft diameter circumference area radius

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Extra Example 3 Find the area and perimeter of the triangle defined by Click to see the triangle. y x Click to see the solutions. Area Perimeter L(-2,-1) (Use the Distance Formula to find KJ and JH.)

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Checkpoint 1. A circular compact disc fits exactly in a square box with sides 12 cm long. Find the diameter, radius, circumference, and area of the CD, and the perimeter and area of the box. Use 3.14 as an approximation for π. Click for the answers. CD: d = 12 cm; r = 6 cm; C 37.7 cm; A 113 cm 2 Box: P = 48 cm; A = 144 cm 2.Find the area and perimeter of the triangle defined by Click for the answers. A = 24 sq. units; P = 24 units

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GOAL 2 USING A PROBLEM-SOLVING PLAN 1.6 Angle Pair Relationships THINK AND DISCUSS: Why do you need a problem-solving plan? Our text provides a 5-step plan as shown on the following slide. You will notice similarities and differences with other plans, and are expected to speak intelligently about these steps as well as use them in your work.

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EXAMPLE 4 A FIVE-STEP PROBLEM-SOLVING PLAN 1.Write a verbal model or draw a sketch. 2. Label your known and unknown facts. 3. Choose definitions, theorems, formulas, or intermediate results you will need to solve the problem. 4. Reason logically to link the information. Use a proof, algebraic equations, or other written argument. 5. Write a conclusion that answers the original problem and check your result.

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Extra Example 4 A maintenance worker needs to fertilize a 9-hole golf course. The entire golf course covers a rectangular area that is approximately 1800 feet by 2700 feet. Each bag of fertilizer covers 20,000 square feet. How many bags will the worker need? 2700 ft 1800 ft Area of field = # of bags Coverage per bag (2700 ft)(1800 ft) = b ft 2 /bag (2700 ft)(1800 ft) 20,000 ft 2 /bag = b 243 bags = b A = bh

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Checkpoint EXAMPLE 5 A painter is painting one side of a wooden fence along a highway. The fence is 926 feet long and 12 feet tall. The directions on each 5-gallon paint bucket say that each bucket will cover 2000 square feet. How may buckets of paint will be needed to paint the fence? Click for the answer. He will need 6 buckets.

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Extra Example 5 EXAMPLE 6 You are designing a mat for a picture. The picture is 8 inches wide and 10 inches tall. The mat is to be 2 inches wide. What is the area of the mat? Click for help. Area of mat = Total area - Area of picture 2 8 in. 2 in. 2 in. 10 in. 2 in. A = b t h t - b p h p

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Extra Example 6 You are making a triangular window. The height of the window is 18 inches and the area should be 297 square inches. How long should the base of the window be? Click for the solution. 18 in. base 297 in. 2 = Area of window Base of window Height of window =

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Checkpoint You are designing a quilt that is made of rectangles sewn together. Each rectangle follows the pattern below. Each of the small triangles has a base of 3 cm and an area of 9 cm 2. 3 cm 1.What is the height of each of the small triangles? 2.What is the area of the border if its width is 3 cm? Click for the answers. h = 6 cm A = 144 cm 2

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QUESTIONS?

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