SOLUTION: Hi a tent has the shape of a triangular prism with dimensions as follows:base 1.6m side edge 1.4m and perpendicular height 1.2m. Height of the prism is 2.5m A find the area of

Question 1088469: Hi
a tent has the shape of a triangular prism with dimensions as follows:base 1.6m side edge 1.4m and perpendicular height 1.2m. Height of the prism is 2.5m
A find the area of material needed to make this tent including the floor area.
B if the material comes in rolls 3.7m wide what length of material must be purchased so that the tent
can be made without any joins except those at the edges.
C if special joining tape is needed to strengthen each join what length of tape will be needed.
I solved part A 12.92 sq m but need help with B and C.
thanks

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The tent in your problem (if it could exist) would look like this
.

B) As you calculated for part A,
the material you need is
a 1.6m by 2.5m rectangle for the floor,
two 1.4m by 2.5m rectangles for the sides, and
two isosceles triangles with 1.6m base and 1.2m height for the front and back.

You could take some grid paper, cut those shapes with a scale of 0.4m=1grid square, and try to fit them into a drawing of the roll of material.

I suspect that you are expected to come up with this (fabric edges in red):
. As you see, you would need to buy a
length of material.

C) You have three 2.5m seams (two between the tent floor and the sides and one joining both sides at the top of the tent roof.
Those seaqms would require of "special joining tape."
You also have 3 seams around the front and 3 around the back triangular pieces.
That would require of "special joining tape."
The total length of of "special joining tape" needed would be
.
Your teacher may expect you to do all those calculations in one long equation, such as
,
or maybe doing your calculations steps by step is preferred.

NOTES:
1) You probably have not yet been taught about the Pythagorean theorem.
If you had learned about it,
you would know that an isosceles triangle with a base measuring ,
and a height of would have leg side lengths such that
,
and that length would be
, not 1.4m.

2) Knowing a bit more math would allow you to be a bit more creative with part B, such as doing this
.
The large green triangle has a vertical side of length and a horizontal side of length .
The small green triangle is a scaled down version of the larger one.
Its vertical side measures
.
That makes it a scale version of the larger green triangle,
so its horizontal side would measure
.
With that arrangement of the tent pieces, the length of fabric you would need to buy would be
.
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