Question 153655: A rectangular light-switch plate is made according to the following dimensions. The length is 7 inches, and the width is 5.5 inches; a rectangular hole measuring 1.2 inches by 0.3 inches is left in the center. (See diagram below) (a) How many square inches in area is the light-switch plate (the shaded region)? (b) If the cost to construct the plate is $4.27 per square inch, what is the construction cost?
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! A rectangular light-switch plate is made according to the following dimensions. The length is 7 inches, and the width is 5.5 inches; a rectangular hole measuring 1.2 inches by 0.3 inches is left in the center. (See diagram below) (a) How many square inches in area is the light-switch plate (the shaded region)? (b) If the cost to construct the plate is $4.27 per square inch, what is the construction cost?
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The area is:
"area border by outside edge of plate" MINUS "area of hole"
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Let's look at each:
"area border by outside edge of plate"
From: "The length is 7 inches, and the width is 5.5 inches"
we get the area (length times width):
7*5.5 = 38.5 square inches
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"area of hole"
From: "rectangular hole measuring 1.2 inches by 0.3 inches"
we get the area (length times width):
1.2 * 0.3 = 0.36 square inches
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So,
"area border by outside edge of plate" MINUS "area of hole"
38.5 - 0.36 = 38.14 square inches (answer for a)
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For part b:
Since the problem stated:
"$4.27 per square inch" we get:
38.14 * 4.27 = $162.86 (answer for b)
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(Sounds like an expensive switch plate to me)
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