SOLUTION: How much canvas is needed to make an A-frame tent that is 4 ft. high with a rectangular floor 6 ft. wide and 9 ft. long

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Question 617113: How much canvas is needed to make an A-frame tent that is 4 ft. high with a rectangular floor 6 ft. wide and 9 ft. long
Found 2 solutions by richwmiller, jsmallt9:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
find the equal hypotenuses
4^2+6^2=c^2
c=2sqrt(13)=7.211
2*2sqrt(13)*9= area=129.799=130 sq ft for the roof
if you want floor too add 54 sq ft 184 sq ft
if you want front and back add 2*1/2 bh=6*4=24 more total 204 sq ft

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
The amount of canvas for the floor is easy: 6*9 = 54 sq. feet.

To find the canvas needed for the sides and the front and the back will take a little effort. For this we need to know the sides of the triangle at the front and back of the tent.

If may help to draw a diagram:
  1. Draw an isosceles triangle. Draw it with a horizontal side, the bottom, and with two congruent diagonals going up to meet at the top of the tent.
  2. Label the bottom edge as a 6, the width of the floor of the tent.
  3. Draw an altitude down from the vertex at the top. Label this altitude as 4 since we're told that the tent is 4 ft. high.
  4. The altitude, by definition, forms a right angle with the bottom edge. So label the angle between the bottom edge and the altitude as a right angle.
  5. Since the altitude was drawn from the vertex formed by the two congruent sides, it will bisect the third side (the bottom). So the two segments of the bottom are going to be 3 each. Label them.
  6. We should now see two right triangles whose legs are 3 and 4. From the Pythagorean Theorem (or just knowing about 3-4-5 right triangle) we can figure out that the two diagonal sides are 5's. Label them.
With our diagram complete, we are now ready to find the rest of the canvas we will need for our tent.

Each of teh diagonal sides of the tent are going to be rectangles with a width of 5 and a length of 9. So each side will be 5*9 or 45 sq. ft. The two sides together will be 90 sq. ft.

It is not clear whether the tent is supposed to have a front and an back. I think yes. The front and the back are triangles. The base of each triangle is 6 and the height is 4. So the area one triangle is %281%2F2%29%286%29%284%29+=+12 sq. ft. This makes the front and back 24 sq. ft.

The total canvas will be the bottom + the sides + the front and back:
Total canvas = 54 + 90 + 24 = 168 sq. ft.