1. Geometry Chapter 1-8 9-3-15 Perimeter, Circumference and Area

2. What we will cover… Perimeter/Circumference Area Base Height Radius Pi, π

3. Perimeter/Circumference Perimeter is the total of the side lengths of a figure with sides made of line segments. Circumference is also the total of the length around a figure but applies only to circles. Perimeter and circumference are measured in linear units like inches, centimeters and miles for example. It may be better to think of perimeter as the shortest distance around a figure (Imagine you had to walk around a rectangle, how far would it be?)

4. Area Area is the number of square units a figure covers. It is the measure of the space covered on a plane. Area is measured in square units, inch 2, centimeters 2 or miles 2 It might help to think of area as how much tile it would take to cover a floor, the tiles are like square units, and when you come to edges, and corners, there are portions of units.

5. Look! If this coordinate plane is made of one inch units, what is the perimeter of figure ABCD? What is the perimeter of triangle PRQ? Find the area of each by counting squares, make your best guess with the partial square units in the triangle (even if you know the formula to find the exact area already)?

6. Look!

7. It makes it easier to illustrate how portions of square units sometimes add up to make whole square units. Just think, if you had to tile the floor of a triangular shaped room, you might have to cut some tiles, but the total of the tiles that actually cover the floor is the area.

8. But how do we really find area? Finding area without overlaying a coordinate plane involves formulas. The formulas are different for every figure, but some categories of figures have formulas that apply to all of the figures of that type. Today we will cover the formulas for the area of a rectangle, a triangle and a circle.

9. Rectangles Rectangles are four sided figures with 4 right angles, the following formula for area will work for all such figures. A=bh or Area=Base times Height You may already be familiar with this, but you should consider the concepts of base and height. In geometry, base and height can be defined by their relationship to eachother. The base is the longest segment perpendicular to height and vice versa. Base? Height? Base? Which is right? Does it matter?

10. Triangles Remember: We can use this for the formula of a triangle. The area of a triangle is: A=1/2bh or Area is one half of the base time the height Notice this formula is the same as the formula for a rectangle, only cut in half. This is because triangles are half of a parallelogram (rectangles are parallelograms). The base is the longest segment perpendicular to height and vice versa.

11. Circles Circles can have perimeter, specifically circumference, and area. The formula for the circumference of a circle is C=2πr. This means: Circumference = 2 times Pi times the distance from the center of the circle to the edge (radius) radius π is the ratio of C/D and is the same For all circles, it is irrational, but we will use 3.14 To calculate values using Pi

12. Circles The area of a circle can be found using the formula A=πr 2 Notice that all the same parts are used: 2, π and r, just in different order.