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S ECTION 1.7 Perimeter, Circumference, and Area

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H OW WOULD WE FIND THE P ERIMETER OF THESE SHAPES ? 7 ft 12 ft 8 in 10 m 35 m

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H OW WOULD WE FIND THE A REA OF THESE SHAPES ? 7 ft 12 ft 5 m 8 in

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H OW WOULD WE FIND THE AREA OF THIS ROOM ? H OW WOULD WE FIND THE PERIMETER ?

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L IST OF FORMULAS SHAPEPERIMETER (P) AREA (A) Squares + s + s + s = 4ss s = s 2 SHAPE PERIMETER ( P )AREA ( A ) Square with side length s s + s + s + s = P = 4 s A = s s = s 2 Triangle with side lengths a, b, and c, base b, and height h P = a + b + cA = ½ b h Rectangle with length l and width w l + l + w + w = P = 2 l + 2 w A = l w Circle with radius r Circumference = C = 2π r A = π r 2

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W HERE TO START ? A PLAN FOR PROBLEM - SOLVING : Ask yourself what you need to solve the problem. Sometimes write down a verbal plan or draw a sketch that will help you find out what you want to know. Label the known and unknown facts. Use labels and facts to choose related definitions, theorems, formulas, or other results you may need. Reason through to link the facts. Write a conclusion that answers the original problem. Check that your answer is logical. Ask yourself what you need to solve the problem. Sometimes write down a verbal plan or draw a sketch that will help you find out what you want to know. Label the known and unknown facts. Use labels and facts to choose related definitions, theorems, formulas, or other results you may need. Reason through to link the facts. Write a conclusion that answers the original problem. Check that your answer is logical.

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E XAMPLE 1: A circular compact disc fits exactly in a square box with sides 12 centimeters long. Find the diameter, radius, circumference, and area of the compact disc, and the perimeter and area of the box. Why would it be helpful for you to know these dimensions? 12 cm.

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E XAMPLE 2: You are planning a deck along two sides of the pool you just put into your backyard. The pool measures 18 feet by 12 feet. The deck is to be 8 feet wide. What is the area of the deck? ft 8 ft 18 ft Area of deck = Area of rectangle 1 + Area of rectangle 3 + the Area of square 2

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