For a roof slope of 12 in 12, the factor to convert plan area to actual area is

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Multiple Choice

For a roof slope of 12 in 12, the factor to convert plan area to actual area is

Explanation:
When a roof is sloped, the plan area (horizontal projection) is smaller than the actual roof surface because the roof is tilted. The conversion uses the roof angle. A 12 in 12 slope means a rise over run of 12:12, which is a 45° angle. The relationship is plan area = actual area × cos(45°). So actual area = plan area ÷ cos(45°) = plan area × sec(45°) = plan area × 1.414. Therefore, the factor to convert plan area to actual area is 1.414.

When a roof is sloped, the plan area (horizontal projection) is smaller than the actual roof surface because the roof is tilted. The conversion uses the roof angle. A 12 in 12 slope means a rise over run of 12:12, which is a 45° angle. The relationship is plan area = actual area × cos(45°). So actual area = plan area ÷ cos(45°) = plan area × sec(45°) = plan area × 1.414. Therefore, the factor to convert plan area to actual area is 1.414.

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