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Question

Difficulty: MediumPerimeter and Area of 2D Figures

A trapezoidal wooden sign has a height of 1818 inches. Its parallel top and bottom edges measure 2424 inches and 3636 inches, respectively. If a rectangular hole measuring 88 inches by 66 inches is cut out of the sign to mount a digital clock, what is the area of the remaining wooden surface in square inches?

Answer: 492 square inches

Answer

492
The remaining area is found by subtracting the area of the inner rectangle from the area of the outer trapezoid. The trapezoid area is 12(24+36)×18=540\frac{1}{2}(24 + 36) \times 18 = 540. The rectangle area is 8×6=488 \times 6 = 48. The difference is 540−48=492540 - 48 = 492.

Step-by-Step Solution

1
Calculate the area of the full trapezoidal sign.
540 square inches
This gives the total area before the hole is cut, using the formula 0.5 * (base1 + base2) * height.
2
Calculate the area of the rectangular cutout.
48 square inches
This represents the area that is removed from the sign, calculated as length * width.
3
Subtract the cutout area from the total area.
492 square inches
Subtracting the removed area from the initial total area gives the area of the remaining solid surface.

Key Concept

Area of composite 2D figures involving trapezoids and rectangles.
Estimated Time:1m 0s
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Topics

Perimeter and Area of 2D Figures

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