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a)
Volume of a prism is given by:
Area of base x height.
color(blue)((2c-2)(3c-4))(2c−2)(3c−4)
b)
(2c-2)(3c-4)=color(blue)(6c^2-14c+8)(2c−2)(3c−4)=6c2−14c+8
c)
(2(2)-2)(3(2)-4)=color(blue)(4)(2(2)−2)(3(2)−4)=4
6(2)^2-14(2)+8=color(blue)(4)6(2)2−14(2)+8=4
d)
The surface area is the sum of all the areas of the 6 faces of the prism. Sides opposite each other have the same area, so there are 3 pairs of areas;
From diagram these are:
2xx(2c-2)(3c-4)=12c^2-28c+162×(2c−2)(3c−4)=12c2−28c+16
2xx(2c-2)(c+7)=4c^2+24c-282×(2c−2)(c+7)=4c2+24c−28
2xx(3c-4)(c+7)=6c^2+34c-562×(3c−4)(c+7)=6c2+34c−56
We add these results together:
color(white)(888)12c^2-28c+1688812c2−28c+16
color(white)(8888)4c^2+24c-2888884c2+24c−28
color(white)(8888)6c^2+34c-5688886c2+34c−56
=color(white)(8)color(blue)(22c^2+30c-68)=822c2+30c−68
