1 Answer

Hilton · Answer 1 · 2023-02-13T00:21:35+0000

Answer:

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

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

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

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

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