Question #11000
Judith works after school at her family's tent company. One of their best selling tents is an A-frame tent that is 4 ft. high and has a rectangular bottom 4ft. wide by 6 ft. long. The sides of the tent are 4.5 ft. long. How much canvas is needed to make the tent?
(Hint: determine the surface area)
(Hint: determine the surface area)
Expert's answer
The tent consists of 5 geometrical figures: 3 rectangles and 2 triangles. The bottom rectangle area is
A1 = width·lenght = 4·6 = 24 ft².
Two other rectangles that make ramps of a tent have area of
A2 = A3 = lenght·√(width²+height²) = 6·√(4²+4²) = 6√32 = 24√2 ft².
Last two triangles that make front and back sides of a tent have area
A4 = A5 = width·height/2 = 6·4/2 = 12 ft².
So, the total area of a needed canvas is
A = A1 + A2 + A3 + A4 + A5 = 24 + 2·24√2 + 2·12 = 48(1+√2) ft².
A1 = width·lenght = 4·6 = 24 ft².
Two other rectangles that make ramps of a tent have area of
A2 = A3 = lenght·√(width²+height²) = 6·√(4²+4²) = 6√32 = 24√2 ft².
Last two triangles that make front and back sides of a tent have area
A4 = A5 = width·height/2 = 6·4/2 = 12 ft².
So, the total area of a needed canvas is
A = A1 + A2 + A3 + A4 + A5 = 24 + 2·24√2 + 2·12 = 48(1+√2) ft².
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