How to find the surface area of a prism

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ISEE Upper Level Quantitative Reasoning › How to find the surface area of a prism

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Find the surface area of a non-cubic prism with the following measurements:

The surface area of a non-cubic prism can be determined using the equation:

Box

The above diagram shows a rectangular solid. The shaded side is a square. In terms of , give the surface area of the box.

$4x^{2} + 30 x$

$15x^{2}$

A square has four sides of equal length, as seen in the diagram below.

Box

All six sides are rectangles, so their areas are equal to the products of their dimensions:

Top, bottom, front, back (four surfaces):

Left, right (two surfaces): $15 \cdot 15 =225$

The total surface area: $4 \cdot 15x + 2 \cdot 225 = 60x + 450$