2. Geometry Review: Basic Concepts of Shapes

3. While the Egyptians and Babylonians demonstrated knowledge about geometry, the Greeks created the first formal mathematics of any kind by organizing geometry with rules of logic. Click here to learn about more math history.

4. Geometry is a fundamental part of mathematics. The word “geometry” comes from the Greek words geo meaning “earth” and metrein meaning “to measure.”

5. Who Uses Geometry? Architects Astronomers Designers: Aeronautical, Graphics, etc. Surveyors Coast Guard And many many more!

6. Basic Properties of Shapes Polygon - an object with many sides. Ex. Triangle, Rectangle, Pentagon, etc. All squares are rectangles, but not all rectangles are squares. Triangles are rectangles cut diagonally in half. The interior angles of a polygon is 360º. The interior angles of a triangle is 180º.

7. Perimeter and Circumference The perimeter (P) of a polygon is the sum of the side lengths. The Circumference (C) is the distance around a circle. To the left are some examples. x x YY P = Y +Y + X+X d = diameter C = 2  r =  d r = radius =2Y + 2X

8. Area of an Object The area (A) of a rectangle is found by multiplying the length (l) by the height (h). The area of a triangle is half of a rectangle. The area of a circle is A = l  h A = ½  l  h A =   r 2 A = 7  5 = 35 5 7 4 5 2 A = ½  4  5 = 10 A =   2 2 = 4 

9. Surface Area The surface area is the sum of area of the faces of an object. (You can find the surface area for a pyramid in a similar manner. Just add the square base and 4 triangular sides!) A face of the cube Surface Area = 4  (4  5) + 2  (6  5) = 4  (20)+ 2  (30) = 80 + 60 =140 5 4 6 4 Faces are (4  5) 2 Faces are (6  5)

10. Volume 5 4 6 The volume, or the amount (of water in this case) you can put in the cube is: V = 6m  4m  5m = 180 m 3. The volume is found by multiplying the length (l) by the width (w) by the height (h). V = l  w  h

11. Volume Cont. The Volume of a Sphere is: V = 4/3    r 3 The Volume of a Square Pyramid is: V = 1/3  l  h 3m V = 4/3    (3m) 3 =4/3    27m 3 = 36  m 3 2m 6m V = 1/3m  2m  6m = 1/3m  12 m 2 = 4 m 3

12. Now Let’s Take The Quiz! Click here to take the Quiz.