1. Perimeter & Area MATH 102 Contemporary Math S. Rook

2. Overview Section 10.3 in the textbook: – Perimeter & area – Pythagorean theorem

3. Perimeter & Area

4. Perimeter & Area in General Perimeter: the sum of the lengths of the sides of a polygon – i.e. the length around (“rim”) the polygon – Measured using the same units as the sides Area: the amount of space inside of the polygon – Measured in square units of the sides On the next few slides are formulas for perimeter and area for common polygons

5. Parallelogram Recall the shape and characteristics of a parallelogram No special formula for perimeter – Just add the lengths of all the sides For a parallelogram with height h and base b, area = h x b – The height is a straight vertical line – See page 471 for theory

6. Trapezoid Recall the shape and characteristics of a trapezoid No special formula for perimeter – Just add up the sides For a trapezoid with lower base b 1, upper base b 2, and height h, area = ½ (b 1 + b 2 ) x h – b 1 and b 2 are parallel to each other – The height h is a straight vertical line

7. Triangle No special formula for perimeter – Just add up the lengths of all the sides For a triangle with a height h and a base b, area = ½ b x h – The height h is a straight vertical line

8. Rectangle & Square Recall that a rectangle has two pairs of corresponding sides each equal in length Given a rectangle with length l and width w: – Perimeter = 2l + 2w – Area = l x w Recall that a square is a rectangle, but with four equal sides – i.e. l and w are the same length Given a square with a sides of length l: – Perimeter = 4l – Area = l 2

9. Circle Recall that the line segment with endpoints at the center of the circle and on the outside of the circle is known as the radius Given a circle with radius r: – Circumference = 2πr Circumference is the circle’s equivalent to perimeter – Area = πr 2 π (pi) is a special constant in mathematics related to the circumference of a circle and its diameter π is infinite so we often approximate it as 3.14

10. Perimeter & Area (Example) Ex 1: Susan wishes to plant Black-Eyed Susans in her circular garden which has a radius of 5 feet. If a package of seeds will cover 12 square feet of her garden, how many whole packages of seeds must Susan buy in order to cover the entire garden?

11. Perimeter & Area (Example) Ex 2: The owners of a 50 foot by 20 foot rectangular field have decided to install a walkway which will border the field. If the walkway extends 5 feet in all directions, find the perimeter of the walkway.

12. Perimeter & Area (Example) Ex 3: Find the area of the shaded region: a) b)

13. Pythagorean Theorem

14. Pythagorean Theorem: given a right triangle with legs a & b and hypotenuse c, the following relationship exists: a 2 + b 2 = c 2 – It does not matter which of the legs is a and which is b – The hypotenuse, c, is the longest side AND is ALWAYS opposite the 90°-angle When solving problems with right triangles, it is often helpful to draw a picture 14

15. Pythagorean Theorem (Example) Ex 4: A 25-foot ladder leans on the roof of a 20 foot-tall building. How far from the building does the base of the ladder extend?

16. Pythagorean Theorem (Example) Ex 5: Find the area of the parallelogram:

17. Summary After studying these slides, you should know how to do the following: – Solve problems involving area & perimeter of common polygons and circles – Understand and apply the Pythagorean Theorem Additional Practice: – See problems in Section 10.3 Next Lesson: – Volume & Surface Area (Section 10.4)