This document provides objectives and examples for finding the perimeter and area of common plane figures such as squares, rectangles, triangles, and circles. It reviews key formulas for perimeter and area, including perimeter formulas for squares (4s), rectangles (2l + 2w), and triangles (a + b + c) and area formulas for squares (s^2), rectangles (lw), triangles (1/2bh), and circles (πr^2). Examples are given for calculating the perimeter and area of specific shapes, including a rectangle, circles, and a triangle using a problem-solving plan approach.

1. Perimeter, Circumference, & Area Objectives: - Find the perimeter and area of common plane figures - Use a general problem solving plan.

2. But first, let’s review angles . . .

4. Reviewing perimeter & circumference Square 4s Rectangle 2l + 2w Triangle a + b + c Circle (circumference) 2πr

5. Reviewing area Square s 2 Rectangle lw Triangle 1/2 bh Circle πr 2

6. Rectangle Get graph paper and draw a 5 by 12 rectangle. Perimeter = 2 l + 2 w = 2*12 + 2*5 = 34 Area = lw = 12*5 = 60

7. Circles Consider a circle with a diameter of 8 cm What is the radius? Circumference = 2πr = 2*3.14*4 = 2.51 cm Area = πr 2 = 3.14*4*4 = 50.2 cm 2

8. Example 3 - Triangle Get graph paper Draw x & y axis Plot points D (1,3) E (8,3) and F (4,7) Draw the height from point F to side DE. Label the point where the height meets DE as G.

9. Example 3 How long is the base? 8 - 1 = 7 How high is the triangle? 7 - 3 = 4 A = 1/2 base * height A = 1/2 * 7 * 4 A = 14 square units

10. A Problem-Solving Plan Ask yourself what you need to solve the problem. Write a verbal model or draw a sketch that will help you find what you need to know. Label known and unknown facts on or near your sketch. Use labels and facts to choose related definitions, theorems, formulas , or other results you may need. Reason logically to link the facts, using a proof or other written argument. Write a conclusion that answers the original problem. Check that your reasoning is correct.

11. Example Look at page 53. Notice the verbal model, labels, & reasoning Check the units Look at examples on p. 54 Follow these guidelines on the test

12. Try problems 3 - 8 Homework: worksheets