Answer: 1360 square cm
===================================================
Step-by-step explanation:
Check out the diagram below.
The original L shape is indicated as "figure A".
Split the L shape into 2 rectangular prisms (aka blocks) labeled figure B and figure C. For now, we'll ignore the red regions, but we'll come back to that later.
Figure B is a block with dimensions of
- L = length = 5
- W = width = 10
- H = height = 30
The surface area is:
SA = 2*(L*W + L*H + W*H)
SA = 2*(5*10 + 5*30 + 10*30)
SA = 1000 square cm
-----------------------
Now move your attention to figure C.
- L = length = 12
- W = width = 5
- H = height = 10
SA = 2*(L*W + L*H + W*H)
SA = 2*(12*5 + 12*10 + 5*10)
SA = 460 square cm.
----------------------
When combining those two surface areas (of figures B and C) we get a total surface area of 1000+460 = 1460 square cm.
But wait, we need to account for those red regions I mentioned earlier.
This region is not frosted as it's inside the cake rather than on the outside.
The area of the red rectangle is 10*5 = 50 sq cm. It's counted twice when we combined the two 3D blocks together to form the L shape again.
So we have to subtract off 2*50 = 100 sq cm to ignore the red region.
1460-100 = 1360 square cm is the final answer.