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The area of the irregularly shaped sheet metal piece in the following figure on the left is to be determined. The longest diagonal is drawn on the figure as shown in the figure on the right. Perpendiculars are drawn to the diagonal from each of the other vertices. The perpendicular segments are measured as shown. From the measurements, the areas of each of the common
The total area of the sheet metal piece.
Answer to Problem 31A
The total area of the sheet metal piece is
Explanation of Solution
Given information:
The height of the triangle shown in part 1 is
Draw the schematic diagram for the sheet metal piece.
Figure -(1)
Write the expression for the area of the part 1.
Here, the height of the triangle shown in part 1 is
Write the expression for the area of the part 2.
Here, the height of the triangle shown in part 2 is
Write the expression for the area of the part 3.
Here, the height of the triangle shown in part 3 is
Write the expression for the area of the part 4.
Here, the height of the part 4 is
Write the expression for the area of the part 5.
Here, the height of the triangle shown in part 5 is
Write the expression for the area of the part 6.
Here, the height of the part 6 is
Write the expression for the area of the part 7.
Here, the height of the triangle shown in part 7 is
Write the expression for the area of the part 8.
Here, the height of the triangle shown in part 8 is
Write the expression for the total area of the sheet metal piece.
Write the expression for the height
Write the expression for the base
Write the expression for the height
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The total area of the sheet metal piece is
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