1. Geometric Measurements Fundamental Tools for Mathematical Modeling

2. Geometric Measurements Perimeter Volume Area

3. Perimeter: The total linear measurement of the curved and/or straight lines bounding a plane area. Area: The measurement of 2 Dimensional planar or curved surfaces expressed in square units. Volume: The amount of space occupied by a three- dimensional object or region of space, expressed in cubic units. Geometric Measurements

4. Perimeter S4S4 S1S1 S2S2 S3S3 Area S1S1 S2S2 Volume Length Width Height S 1+ S 2+ S 3 + S 4 = Perimeter S 1 x S 2 = Area Length x Width x Height = Volume

5. Perimeter Calculate the Perimeter of a Football Field From goal line to goal line S4S4 S1S1 S2S2 S3S3 S 1 S 2 S 3 S 4 + = Perimeter End Zone 300’ 150’ Goal Lines

6. Circumference The Perimeter of a Circle Radius = 0.250” Diameter = 2R = 0.500” D a = 3.14

7. Calculating the Perimeter of a Triangle 4.0” 6.0” 3.0” 5.0” a b c S1 S2 S3 Note: Segment ba is congruent to segment bc and segment da is congruent to segment dc. That information is given in the figure. d S1 + = Perimeter

8. AREA Calculate the Playing Area of a Football Field From goal line to goal line S2S2 S1S1 End Zone 300’ 150’ Note: 1 acre = 43,560 square foot

9. The Area of a Circle Radius = 0.250” Diameter = 2R = 0.500” D a = 3.14 Note: This is a small circle with a radius equal to that of the corner radius of the GEARS-IDS 6x9 Plate.

10. Calculating the Area of a Triangle Note: Segment ba is congruent to segment bc and segment da is congruent to segment dc. That information is given in the figure. 4.0” 6.0” 3.0 ” 5.0” a b c S1 S2 S3 d

11. Volume Calculate the Volume of a 2’ Snow Covering From goal line to goal line S2S2 S1S1 End Zone 300’ 150’ Volume is the product of 3 values;Length, Width and Depth and is expressed in cubic feet, or ft 3

12. The Volume of a Cylinder V(cyl) =  r 2 R = 0.095” H = 0.090” Note: This is a very small cylinder. These are the dimensions of the holes in the GEARS-IDS 6x9 Plate H R

13. Calculate the Perimeter of the 6” x 9” Plate = 3.14 Corner Radius =0.250” 5.688” 8.688” Note: To solve this problem accurately it is necessary to calculate the perimeter of the corners.

14. Calculate the Area of the 6” x 9” Plate = 3.14 Corner Radius =0.250” 5.688” 8.688” Note: A precise solution to this problem requires breaking the area up into multiple small areas Don’t forget to subtract the area of all the holes! Hole Dia. 0.190”

15. Calculate the Volume of the 6” x 9” Plate = 3.14 Corner Radius =0.250” 5.688” 8.688” Note: The solution to this problem is dependent on calculating the area accurately! Hole Dia. 0.190” Plate Thickness 0.090”

16. Density Using Volume to Calculate Weight The DENSITY of a material is expressed as the weight of the material per unit of volume. Density = Weight / Volume Weight = Density x Volume MaterialDensity lbs./ft 3 Aluminum168.5 Steel489 Water62.4 Air0.0807

17. Calculate the Weight of the 6” x 9” Plate = 3.14 Corner Radius =0.250” 5.688” 8.688” Note: The solution to this problem is dependent on calculating the Volume accurately! Hole Dia. 0.190” Plate Thickness 0.090” Density of Al = ( approximately) 1.56 oz/ in 3 Check your calculations by weighing the plate!

18. Volume of Solids r h V =  r 2 h V = s 3 s s s h w l V = lwh r V = (4/3)  r 3 Quick Reference Slide

19. Perimeter and Area of Basic Shapes b h s P = s 1 + s 2 + s 3 A = ½ bh s s Perimeter = 4s or s+s+s+s Area = s 2 l w P = 2l+2w or 2(l+w) or l+w+l+w A = lw r C = 2  r =  d A =  r 2 Quick Reference Slide

20. Go Forth and Calculate, The End For Now