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Difficulty: MediumPerimeter and Area of 2D Figures

An artist is framing a rectangular painting that measures 1010 inches in length and 88 inches in width. The frame has a uniform width of 22 inches on all sides. What is the total area of the frame itself, in square inches?

Answer: 88 square inches

Answer

88
To find the area of the frame, subtract the area of the painting from the total area of the painting with the frame included. Because the frame is 2 inches wide on all sides, the overall dimensions increase by 4 inches in both directions. The outer rectangle is 14 inches by 12 inches (168 square inches). The inner painting is 10 inches by 8 inches (80 square inches). Subtracting the inner area from the outer area gives 168 - 80 = 88 square inches.

Step-by-Step Solution

1
Determine the outer dimensions of the framed painting.
Outer length = 14 inches, Outer width = 12 inches
The frame adds 2 inches to both the left and right sides (total of 4 inches to length), and 2 inches to both the top and bottom (total of 4 inches to width).
2
Calculate the total combined area of the painting and the frame.
168 square inches
Area of a rectangle is length multiplied by width (14 * 12).
3
Calculate the area of the inner painting.
80 square inches
The painting dimensions are 10 by 8 (10 * 8).
4
Subtract the inner area from the total area to find the area of the frame.
88 square inches
The frame is the region between the outer and inner rectangles.

Key Concept

The area of a border or frame is found by calculating the total outer area and subtracting the inner area.
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Topics

Perimeter and Area of 2D Figures

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