1.7 Introduction to Perimeter, Circumference, and Area Geometry

Perimeter vs Area Perimeter is the distance around the shape Area is the amount of space the shape takes up….what is inside

SQUARE Side length s Perimeter (P) P = 4s Area (A) A = s 2

RECTANGLE Length l and width w Perimeter (P) P = 2 l + 2w Area (A) A = l w

TRIANGLE

CIRCLE Radius r Circumference (C) C = 2πr Area (A) A = πr²

Example 1 Find the perimeter and area of a rectangle of length 4.5m and width 0.5m

Solution Area A = l w A = (4.5)(.5) A = 2.25 m 2 Perimeter P = 2 l + 2w P = 2(4.5) + 2(.5) P = P = 10 m

Example 2 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 6 feet high. Find the diameter, radius, circumference, and area of the circle. Answers must be exact (no decimals).

Example 3 Find the area and perimeter of the triangle defined by H(-2, 3), J(3, -1), K(-2, -4).

Example 4 Find the area and perimeter of the triangle defined by T(-2, 6), U(4, 6), and V(4, -2).

PROBLEM SOLVING PLAN 1.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. 2.Label known and unknown facts on or near your sketch. 3.Use labels and facts to choose related definitions, theorems, formulas, or other results you may need. 4.Reason logically to link the facts, using a proof or other written argument. 5.Write a conclusion that answers the original problem. Check that your reasoning is correct.

Example 5 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?

Example 6 You are designing a mat for a picture (a mat goes around the perimeter of the 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?

Example 7 You are making a triangular window. The height of the window is 18 inches and the area should be 297 inches. What should the base of the window be.

Example 8 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 can say that each can will cover 2000 square feet. How many cans of paint will be needed to paint the fence?

Example 9 You are planning a deck along two adjacent sides of a pool. The pool measures 18 feet by 12 feet. The deck is to be 8 feet wide. What is the area of the deck?

Example 10 You are making a triangular flag with a base of 24 inches and an area of 360 square inches. How long should it be.