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Geometric Measurements Fundamental Tools for Mathematical Modeling

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Geometric Measurements Area

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The measurement of planar or curved surfaces expressed in square units. Geometric Measurements Area:

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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

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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.

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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

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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”

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The Surface Area of a Cylinder h r Length = Circumference Parts of a Cylinder = 2 Circles + 1 Rectangle Area of a Circle x 2 Area of a Rectangle with Circumference as length

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Calculate the Surface Area of a Gear Head Motor 2.00” Dia. 1.55” 3.850” 1.367”

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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

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Go Forth and Calculate, The End For Now

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Section 1.7. Recall that perimeter is the distance around a figure, circumference is the distance around a circle, and area is the amount of surface covered.

Section 1.7. Recall that perimeter is the distance around a figure, circumference is the distance around a circle, and area is the amount of surface covered.

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