Answer:
(d) 9 ft²
Explanation:
To find the excluded area for furniture, we can find the actual size of the door, then compute the area of the semicircle that it turns through. The door size will be the product of the drawing dimension and the scale factor relating the room to the drawing.
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door size
Room size and drawing size are proportional. This means ...
door size / door drawing = room length / room drawing
door size / (1.75 in) = (15 ft)/(11 in)
door size = (15 ft)(1.75/11) = 105/44 ft ≈ 2.386 ft
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exclusion area
The area of a circle with radius r is given by the formula ...
A = πr²
Then the area of a semicircle (half a circle) with radius 2.386 ft will be ...
A = 1/2π(2.386 ft)² ≈ 8.945 ft²
A good estimate of the furniture exclusion area is 9 ft².
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Additional comment
The scale factor is (15 ft)/(11 in) = 15/11 ft/in. Multiplying that by 7/4 in gives 105/44 ft.