Question

4.6 surface area of prisms and cylinders
you are a manufacturer who manufactures tents. how many square inches of material is needed to make the tent below?
50 in 80 in
square inches of material is needed.
most material is purchased by the square yard. there are 1,296 square inches in 1 square yard. divide your answer by 1296 and tell me how many square yards you will need. (round your answer to the nearest whole number.)
i will need square yards.

Explanation:

Step1: Identify the tent as a triangular - prism and find the area of the triangular bases.

The base of the triangular - prism is a right - triangle with legs $a = 50$ in and $b = 60$ in. The area of a triangle is $A_{triangle}=\frac{1}{2}ab$. So, $A_{triangle}=\frac{1}{2}\times50\times60 = 1500$ square inches. Since there are 2 triangular bases, the total area of the bases is $2\times1500=3000$ square inches.

Step2: Find the area of the rectangular faces.

There are 3 rectangular faces.
Face 1: With dimensions $60$ in (height of the prism) and $80$ in. Its area $A_1 = 60\times80=4800$ square inches.
Face 2: With dimensions $50$ in and $80$ in. Its area $A_2 = 50\times80 = 4000$ square inches.
Face 3: First, find the hypotenuse of the base triangle using the Pythagorean theorem $c=\sqrt{a^{2}+b^{2}}=\sqrt{50^{2}+60^{2}}=\sqrt{2500 + 3600}=\sqrt{6100}\approx78.1$ in. The area of the third rectangular face with dimensions $78.1$ in and $80$ in is $A_3\approx78.1\times80 = 6248$ square inches.
The total area of the rectangular faces is $A_{rect}=4800 + 4000+6248=15048$ square inches.

Step3: Calculate the total surface area of the tent.

The total surface area of the prism $A = A_{bases}+A_{rect}=3000 + 15048=18048$ square inches.

Step4: Convert square inches to square yards.

Since there are 1296 square inches in 1 square yard, the number of square yards is $\frac{18048}{1296}\approx14$ square yards.

Answer:

18048 square inches of material is needed.
I will need 14 square yards.