To find the amount of wood Zeke uses to make the frame, we need to calculate the area of the frame, which includes both the area of the picture and the area of the frame itself.
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Dimensions of the picture:
- Width = 5 inches
- Height = 7 inches
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Dimensions of the frame: The frame is 3/4 inch wide on all sides. To find the overall dimensions of the frame, we need to add twice the width of the frame to each dimension of the picture (since the frame surrounds the picture on both sides).
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Overall Width of the frame = 5 inches + 2 * (3/4 inch)
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Overall Width = 5 inches + 1.5 inches
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Overall Width = 6.5 inches
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Overall Height of the frame = 7 inches + 2 * (3/4 inch)
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Overall Height = 7 inches + 1.5 inches
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Overall Height = 8.5 inches
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Area of the picture: \[ \text{Area of the picture} = \text{Width} \times \text{Height} = 5 \text{ inches} \times 7 \text{ inches} = 35 \text{ square inches} \]
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Area of the frame: \[ \text{Area of the frame} = \text{Overall Width} \times \text{Overall Height} = 6.5 \text{ inches} \times 8.5 \text{ inches} = 55.25 \text{ square inches} \]
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Area of the wood used: To find the area of the wood used, subtract the area of the picture from the area of the frame: \[ \text{Area of the wood} = \text{Area of the frame} - \text{Area of the picture} = 55.25 \text{ square inches} - 35 \text{ square inches} = 20.25 \text{ square inches} \]
Thus, Zeke uses 20.25 square inches of wood to make the frame.
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