What is the lateral area of a prism which has a lateral edge of 4 inches and has a regular pentagonal base with an edge of 12 in
ches?
1 answer:
Check the picture below.
so the pentagonal prism in the picture is been seen from the bottom, namely so we can see its base, however the base is at the bottom, what does that mean, it means that the pentagonal bases are the top and bottom of the prism, that matters, because the other sides are the lateral sides.
so, if we notice, the lateral sides are really just 5 rectangles, each one a 12x4, so if we simply get the area of all those rectangles.
5(12 * 4) = 240 in².
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Part 1
<h3>Answer: (x+5)(x+10) - 50 = 126</h3>Other answers are possible.
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Explanation:
The old width was 5, but then it increases to x+5. The old length was 10, but now it's x+10.
The area of any rectangle is length times width.
So the area of the larger rectangle is (x+5)(x+10). Subtract off the old area of 5*10 = 50 and we get (x+5)(x+10) - 50 as the area of the L shape. Set this equal to 126 to finish setting up the equation. This is one possible answer out of many others. This is because we could expand out the (x+5)(x+10) into x^2+10x+5x+50 or simplify that to x^2+15x+50, as two possible options.
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Part 2
<h3>Answer: x = 6</h3>-------------
Explanation:
Solve the equation we set up in the previous part
(x+5)(x+10) - 50 = 126
x^2+10x+5x+50-50 = 126
x^2+15x = 126
x^2+15x-126 = 0
Apply the quadratic formula from here
Another method you could use is factoring, so you could say:
x^2+15x-126 = 0
(x-6)(x+21) = 0
x-6 = 0 or x+21 = 0
x = 6 or x = -21
The issue with this is that it may take a while to do this trial and error approach.
Whichever method you used, you'll end up with two solutions. One of those solutions doesn't make sense though. We can't have a negative length or distance value, so we ignore x = -21.
The only practical solution is x = 6
If x = 6, then the old height goes from 5 to x+5 = 6+5 = 11
If x = 6, then the old length goes from 10 to x+10 = 6+10 = 16
The new larger rectangle is 11*16 = 176 sq ft, in which we subtract off the 50 sq ft to get 176-50 = 126 sq ft, and this matches with the 126 given to us. Therefore, the answer is confirmed.