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NO LINKS!!! Part 2: Find the Lateral Area, Total Surface Area, and Volume. Round your answer to two decimal places.​

NO LINKS!!! Part 2: Find the Lateral Area, Total Surface Area, and Volume. Round your-example-1
User BBlackwo
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Answer:

Question 7

Lateral Surface Area

The bases of a triangular prism are the triangles.

Therefore, the Lateral Surface Area (L.A.) is the total surface area excluding the areas of the triangles (bases).


\implies \sf L.A.=2(10 * 6)+(3 * 6)=138\:\:m^2

Total Surface Area

Area of the isosceles triangle:


\implies \sf A=(1)/(2)* base * height=(1)/(2)\cdot3 \cdot √(10^2-1.5^2)=(3√(391))/(4)\:m^2

Total surface area:


\implies \sf T.A.=2\:bases+L.A.=2\left((3√(391))/(4)\right)+138=167.66\:\:m^2\:(2\:d.p.)

Volume


\sf \implies Vol.=area\:of\:base * height=\left((3√(391))/(4)\right) * 6=88.98\:\:m^3\:(2\:d.p.)

Question 8

Lateral Surface Area

The bases of a hexagonal prism are the pentagons.

Therefore, the Lateral Surface Area (L.A.) is the total surface area excluding the areas of the pentagons (bases).


\implies \sf L.A.=5(5 * 6)=150\:\:cm^2

Total Surface Area

Area of a pentagon:


\sf A=(1)/(4)\sqrt{5(5+2√(5))}a^2

where a is the side length.

Therefore:


\implies \sf A=(1)/(4)\sqrt{5(5+2√(5))}\cdot 5^2=43.01\:\:cm^2\:(2\:d.p.)

Total surface area:


\sf \implies T.A.=2\:bases+L.A.=2(43.01)+150=236.02\:\:cm^2\:(2\:d.p.)

Volume


\sf \implies Vol.=area\:of\:base * height=43.011193... * 6=258.07\:\:cm^3\:(2\:d.p.)

User Hilton
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