Math for Welders, 5th Edition Page 159 (159 of 288)

159
Unit 17 Four-Sided Measure
Copyright by The Goodheart-Willcox Co., Inc.
Area of a Trapezoid
Use the following steps to calculate the area of a trapezoid.
1. Add the two parallel lengths.
331 + 262 = 593
2. Multiply by the height.
593
×
204 = 120972
3. Divide by 2.
120972
÷
2 = 60486 mm
As stated previously, geometric shapes are often related. If you make two trapezoids of
the same size, rotate one of them 180°, and then butt them end to end, you will have formed a
parallelogram that is twice the size of the original trapezoid.
Converting Square Units of Measure
In the welding trade, the most common units of square measure are square feet, square
inches, and square millimeters. Each unit of measure can be converted to the other units.

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159
Unit 17 Four-Sided Measure
Copyright by The Goodheart-Willcox Co., Inc.
Area of a Trapezoid
Use the following steps to calculate the area of a trapezoid.
1. Add the two parallel lengths.
331 + 262 = 593
2. Multiply by the height.
593
×
204 = 120972
3. Divide by 2.
120972
÷
2 = 60486 mm
As stated previously, geometric shapes are often related. If you make two trapezoids of
the same size, rotate one of them 180°, and then butt them end to end, you will have formed a
parallelogram that is twice the size of the original trapezoid.
Converting Square Units of Measure
In the welding trade, the most common units of square measure are square feet, square
inches, and square millimeters. Each unit of measure can be converted to the other units.

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Copyright by The Goodheart-Willcox Co., Inc.
158
Section 4 Measurement
Notice it is not the length and the width that are being multiplied, but the length of one
side and the height. You may find it interesting to note that geometric shapes are often closely
related. If you were to cut the parallelogram below along the dotted line and then reassemble
it as shown, you would have created a rectangle. This is why the area of a parallelogram is
calculated by multiplying the length and the height.
Trapezoid
The trapezoid, like all the shapes studied so far, has four sides. Two of the sides are parallel,
but the other two sides are not parallel to each other. For this reason, a trapezoid is not as
symmetric or pleasing to look at as a parallelogram. Also, it does not appear in fabrication and
construction as often as the parallelogram.
Height
Perimeter of a Trapezoid
To calculate the perimeter of a trapezoid, add the four sides.
P = 54″ + 100″
″
+ 64″
″
+ 82″
″
P = 300″

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Copyright by The Goodheart-Willcox Co., Inc.
160
Section 4 Measurement
Square Feet to Square Inches
A square with sides measuring 1′ has an area of one square foot. Since 1′ equals 12″, the ″
square also has an area of 12″ × 12″ or 144 in2. ″
Therefore, to change square feet to square inches, multiply the number of square feet by 144.
1 ft2 = 1
×
144 = 144 in2
Square Inches to Square Feet
To convert square inches to square feet, divide the number of square inches by 144.
1. 144 in2 = 144 ÷ 144 = 1 ft2
2. 1,000 in2 = 1,000 ÷ 144 = 6.9 ft2 (rounded)
3. 3,600 in2 = 3,600 ÷ 144 = 25 ft2
Square Inches to Square Millimeters
A square with sides measuring one inch has an area of one square inch. Since 1″ equals ″
25.4 mm, the square also has an area of 25.4 mm × 25.4 mm or 645.16 square millimeters (mm2).

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Page 9Section 1 Whole Numbers click to expand contents

Page 57Section 2 Common Fractions click to expand contents

Page 101Section 3 Decimal Fractions click to expand contents

Page 131Section 4 Measurement click to expand contents

Page 193Section 5 Volume, Weight, and Bending Metal click to expand contents

Page 241Section 6 Percentages and the Metric System click to expand contents

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