
The area of the template.

Answer to Problem 64A
Area
Explanation of Solution
Concept used:
The template is divided into two trapeziums and a rectangle as shown.
The area of two trapeziums and the area of rectangle are added to find the required area.
Calculation:
Area of trapezium (1),
Here, height h = 215 − 100 = 115 mm, base b1= 310 mm and
Base (b2) is calculated as:
Since the groove makes an angle of 28° then, the angle made by the triangle is,
Thus, from symmetry the base of another triangle is also 61.2 mm.
Now, the base b2 of the trapezium is:
Substituting the above values in the formula;
Again, Area of trapezium (2),
Here, height h = 85 mm,
Base b1is calculated as:
Since the groove makes an angle 28°, then the
Hence,
Again, From the geometry of the figure the line BCE makes an angle of 90° and
Now, the combined
Thus, from symmetry the base of another triangle is also 57.33 mm.
Now, the base b2 of the trapezium is:
Substituting the above values in the formula;
Area of rectangle
Here, length l = 310 mm and Width w = 100 mm
By substituting the above values in the formula;
Now, Adding the equations (1), (2), and (3) to calculate the required area.
Thus,
Conclusion:
Thus, the area of the given template is
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Chapter 59 Solutions
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