Surface Area of a Rectangular Prism

[5th Grade Teacher]

Hey... I'm hoping y'all can help me out with this problem. I'm working on surface area for a staff development class and was presented this problem:

A team of students is making a large model of a high-rise building for a project on architecture. The model consists of a rectangular prism with a square base. The top of the building is a pyramid with a square base that covers the top of the rectangular prism. The model is 1 foot wide and 5 feet high to the base of the pyramid. The slant height of the faces of the pyramid (triangles) is 5/8 foot, or 7.5 inches. The students want to cover their model with green paper. What is the surface area that they will need to cover?

To find the surface area of the rectangular base I would multiple L x W right? But wouldn't that be 1 x 1? Now I'd have to find the surface of one of the sides 1/2 of L x W, so half of 5 x 7.5 equals 18.75. Now I have four of those sides, so it would be (18.75 x 4) + 1 = 76. Am I on the right track? I feel like I've messed up. Thanks!

 

[galactus]

The rectangular prism tower has surface area (1)(5)(4)=20.

The pyramid has base 1 and height 0.625 feet. It can be broken up into 4 triangles of height 0.625 feet and base 1.

\(\displaystyle \L\\4\cdot{\frac{0.625}{2}}=1.25\)

Total surface area is 21.25.

I did not calculate a base for the tower or the pyramid, because I assume they won't be covered.

 

[soroban]

Hello, 5th Grade Teacher!

Do you make any sketches?

A team of students is making a large model of a high-rise building for a project on architecture.
The model consists of a rectangular prism with a square base.
The top of the building is a pyramid with a square base that covers the top of the rectangular prism.

The model is 1 foot wide and 5 feet high to the base of the pyramid.
The slant height of the faces of the pyramid (triangles) is 5/8 foot, or 7.5 inches.
The students want to cover their model with green paper.
What is the surface area that they will need to cover?

The rectangular prism looks like this:

         *-----*
        /     /|
       /     / |
      *-----*  | 5
      |     |  |
      |     |  |
    5 |     |  *
      |     | /
      |     |/1
      *-----*
         1

Only the four sides will be covered.
The sides are each 1 × 5 rectangles with an area of 5 ft².
The four sides have a total area of: \(\displaystyle \:4\,\times\,5 \:=\:\fbox{20\text{ ft}^2}\)


The faces of the square pyramid look like this:

            *
           /|\
          / | \
         /  |h \ 0.625
        /   |   \
       /    |    \
      *-----*-----*
              0.5

From the right triangle, we have: \(\displaystyle \:h^2\,+\,(0.5)^2\:=\0.625)^2\)
. . from which we get: \(\displaystyle \:h \:=\:0.375\) ft

Each triangle has area: \(\displaystyle \;\frac{1}{2}(1)(0.375) \:=\:0.1875\) ft².
The four triangles have a total area of: \(\displaystyle \,4\,\times\,0.1875 \:=\:\fbox{0.75\text{ ft}^2}\)


Therefore, the total surface area is . . .

 

[galactus]

Oh, I interpreted differently. I used 0.625 as h.

 

[Denis]

galactus, as penance, recite the Hoooooly Rosary twice, and fervently :evil: