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The volume of the prism is 144 ft^3. If we use the letter V to represent volume, the formula for the volume of a rectangular prism is V=length*width*height. When you plug in the numbers, the equation is V=12*6*2. When you multiply these three numbers together, you get 144. Because you are finding the volume, your units are cubed, so your answer is 144 ft^3. I have attached an image of this problem written out (I’m sorry if the image is bad, I drew it on my phone). If you need any more help or any clarification, please let me know and I will be happy to help!
Answer:
See below.
Step-by-step explanation:
Top prism:
To find the volume of the top prism, multiply the area of the base by the height. This is 1/2 times width times height times length.
V =1/2 l*w*h =1/2* 3*2.8*8 = 33.6
To find the surface area of a prism, find the area of the triangular base and the area of each rectangular side.
Area of the base is A = 1/2 * b*h = 1/2 * 3 * 8 = 12. Since there are 2 bases, the area is 24.
Area of the rectangular side is A = b*h = 2.8*5 = 14. Since there are two, the area is 2*14 = 42.
The surface area of the prism is 24 + 28 = 52.
Bottom prism:
To find the volume of the bottom prism, multiply the width times the height times the length.
V = l*w*h = 8*2.8*4.8 = 107.52
To find the surface area of the bottom prism, find the area of the base and each side of the house.
A = 8*2.8 = 22.4
A = 8*4.8 = 38.4 which occurs twice so it has a total area of 76.8
A = 2.8*4.8 = 13.44 which occurs twice so it has an area of 26.88.
The total volume is 33.6 + 107.52 = 141.12
The total surface area is 52 + 22.4 + 76.8 + 26.88 = 178.08
