SOLUTION: How to find the surface area of the solid. The pyramids are regular, and the prisms, cylinders and cones are right. Please refer to the textbook ISBN 0669 45530-X Geometry: An In

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Question 204016This question is from textbook Geometry: An Integrated Approach
: How to find the surface area of the solid. The pyramids are regular, and the prisms, cylinders and cones are right.
Please refer to the textbook ISBN 0669 45530-X Geometry: An Integrated Approach
1998 Chapter 12 section 3 Problem # 23
This problem has a rectangle (as a tower) and on the top it has a pyramids. I tried many time to find the answer but I did not find the correct way to do it. PLease help me!
Thank you! This question is from textbook Geometry: An Integrated Approach

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
I don't have a copy of the cited text book but I can give you some guidance for finding the surface area of the solid figure you have described.
You will need to do this kind of problem in two parts then add the two results for you final answer.
Part 1)
Find the surface area of a rectangular prism whose base dimensions are L and W and whose height is h.
Notice that the rectangular prism consists of four rectangles (2 pairs of congruent (identical) rectangles.
The surface area of one pair of the congruent rectangles is found by:
A+=+2%28L%2Ah%29 and, for the other pair:
A+=+2%28W%2Ah%29
Add these together to get the total surface area (also called lateral surface area) of the rectangular prism.
Step 2).
Find the surface area of the rectangular pyramid.
Usually, you are given the perpendicular height of the pyramid but you may also be given the slant height.
If you are given the slant height, then finding the surface area (lateral area) is a lot easier.
A+=+%281%2F2%29P%2Ash where P = perimeter of the base and sh = slant height.
To find the slant height (sh) when you are given the perpendicular height (h), use:
sh+=+sqrt%28h%5E2%2B%28W%2F2%29%5E2%29 for one pair of congruent faces, and...
sh+=+sqrt%28h%5E2%2B%28L%2F2%29%5E2%29 for the othe pair of congruent faces.
Add these together to get the total surface area of the pyramid.
Finally, add the surface area of the rectangular prism to the suface area of the rectangular pyramid to get the total surface area of the figure.