<span><span>(<span>6−d</span>)</span><span>(<span><span><span>d^2</span>−5</span>+<span>3d</span></span>)</span></span><span>=<span><span>(<span>6+<span>−d</span></span>)</span><span>(<span><span><span>d^2</span>+<span>−5</span></span>+<span>3d</span></span>)</span></span></span><span>=<span><span><span><span><span><span><span>(6)</span><span>(<span>d^2</span>)</span></span>+<span><span>(6)</span><span>(<span>−5</span>)</span></span></span>+<span><span>(6)</span><span>(<span>3d</span>)</span></span></span>+<span><span>(<span>−d</span>)</span><span>(<span>d^2</span>)</span></span></span>+<span><span>(<span>−d</span>)</span><span>(<span>−5</span>)</span></span></span>+<span><span>(<span>−d</span>)</span><span>(<span>3d</span>)</span></span></span></span><span>=<span><span><span><span><span><span>6<span>d^2</span></span>−30</span>+<span>18d</span></span>−<span>d^3</span></span>+<span>5d</span></span>−<span>3<span>d^2</span></span></span></span><span>
=<span><span><span><span> −<span>d3^</span></span>+<span>3<span>d^2</span></span></span>+<span>23d</span></span>−<span>30</span></span></span>
<span>
</span>
Lateral surface area of the prism = 920 in²
Total surface area of the prism = 1180 in²
Solution:
Length of the prism = 13 in
Width of the prism = 10 in
Height of the prism = 20 in
Lateral surface area of the prism = 2(l + w)h
= 2(13 + 10) × 20
= 2(23) × 20
= 920 in²
Lateral surface area of the prism = 920 in²
Total surface area of the prism = Lateral area + 2lw
= 920 + 2 × 13 × 10
= 920 + 260
Total surface area of the prism = 1180 in²
Hence Lateral surface area of the prism = 920 in²
Total surface area of the prism = 1180 in²
Compare 100 to 110, and see that to go from 100 to 110 is a 10% increase, but to go from 110 back down to 100 is a 9.09% decrease not a 10% decrease
