Rewrite f(x)=-3(x+1)^2+27 in intercept form
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Check the picture below.
the "lateral" area, or "sides" area, is just the area of all the four triangular faces, and it doesn't include the bottom or base of the pyramid.
however, notice, each triangular face is really just a triangle with a base of 24, and a height of 16.
![\bf \left[\frac{1}{2}(\stackrel{b}{24})(\stackrel{h}{16}) \right]+\left[\frac{1}{2}(\stackrel{b}{24})(\stackrel{h}{16}) \right]+\left[\frac{1}{2}(\stackrel{b}{24})(\stackrel{h}{16}) \right]+\left[\frac{1}{2}(\stackrel{b}{24})(\stackrel{h}{16}) \right] \\\\\\ \textit{or just }\qquad 4\left[\frac{1}{2}(\stackrel{b}{24})(\stackrel{h}{16}) \right]\impliedby \textit{lateral area of the pyramid}](https://tex.z-dn.net/?f=%5Cbf%20%5Cleft%5B%5Cfrac%7B1%7D%7B2%7D%28%5Cstackrel%7Bb%7D%7B24%7D%29%28%5Cstackrel%7Bh%7D%7B16%7D%29%20%5Cright%5D%2B%5Cleft%5B%5Cfrac%7B1%7D%7B2%7D%28%5Cstackrel%7Bb%7D%7B24%7D%29%28%5Cstackrel%7Bh%7D%7B16%7D%29%20%5Cright%5D%2B%5Cleft%5B%5Cfrac%7B1%7D%7B2%7D%28%5Cstackrel%7Bb%7D%7B24%7D%29%28%5Cstackrel%7Bh%7D%7B16%7D%29%20%5Cright%5D%2B%5Cleft%5B%5Cfrac%7B1%7D%7B2%7D%28%5Cstackrel%7Bb%7D%7B24%7D%29%28%5Cstackrel%7Bh%7D%7B16%7D%29%20%5Cright%5D%0A%5C%5C%5C%5C%5C%5C%0A%5Ctextit%7Bor%20just%20%7D%5Cqquad%204%5Cleft%5B%5Cfrac%7B1%7D%7B2%7D%28%5Cstackrel%7Bb%7D%7B24%7D%29%28%5Cstackrel%7Bh%7D%7B16%7D%29%20%5Cright%5D%5Cimpliedby%20%5Ctextit%7Blateral%20area%20of%20the%20pyramid%7D)
the "lateral" area, or "sides" area, is just the area of all the four triangular faces, and it doesn't include the bottom or base of the pyramid.
however, notice, each triangular face is really just a triangle with a base of 24, and a height of 16.