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Find the surface area of each right prism with the given features. Round to the nearest whole number. a. The bases are equilateral triangles with sides of length 8 ft, and the height of the prism is 10 ft. b. The bases are trapezoids with parallel sides of lengths 7 cm and 9 cm perpendicular to one side of length 6 cm. The height of the prism is 12 cm.

Mathematics
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  • S
|dw:1331704594631:dw| So you have 2 triangles and 3 rectangles.. find the area of each and add up.. (area of a triangle) times 2 (cause you have 2 of them) + (area of a rectangle) times 3 (cause you have 3 of them) |dw:1331704935273:dw| a^2 + b^2 = c^2 4^2 + h^2 = 8^2 16 + h^2 = 64 h^2 = 48 h = sqrt(48) Now we can find the area of the triangle (1/2)(base)(height) = (1/2)*(4)*(sqrt(48)) = 13.86 Now lets find the area of a rectangle Side * side = 8 * 10 = 80 Now lets plug in to our original formula 2*(13.86) + 3*(80) = 267.72 = 268 square feet
  • S
|dw:1331705524042:dw| Here, we find the area of a trapezoid, multiply by 2, cause we have two of them, plus, the areas of each of the faces (front, back, left, right) So area of a trapezoid: ((base1+base2)/2)*height = ((9 + 7)/2) * 6 = 48 Now, we have to find the areas of each of the faces.. so its 9*12, 6*12, 7*12, and we have one missing, so lets find that: |dw:1331706007160:dw| a^2 + b^2 = c^2 2^2 + 6^2 = c^2 4 + 36 = c^2 40 = c^2 c = sqrt(40) So the total surface area is: 48*2 + 9*12 + 6*12 + 7*12 + sqrt(40) * 12 = 435.89 = 436 square feet
@S The answer in the book says its exactly 295ft for letter a

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  • S
OOops.. sorry.. a^2 + b^2 = c^2 4^2 + h^2 = 8^2 16 + h^2 = 64 h^2 = 48 h = sqrt(48) Now we can find the area of the triangle (1/2)(base)(height) = (1/2)*(8)*(sqrt(48)) = 27.71 Now lets find the area of a rectangle Side * side = 8 * 10 = 80 Now lets plug in to our original formula 2*(27.71) + 3*(80) = 295.42 = 295 square feet
  • S
Instead of using 8 as a base when calculating the area of the triangle, I used 4.
  • S
Now it comes out to 295
  • S
Do you understand it though?
yes thank you
  • S
You are welcome

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