Find the total surface area of a right rectangular prism...

Find the total surface area of a right rectangular prism with the given dimensions.
a $\ell=15 \mathrm{cm}, w=5 \mathrm{cm}, h=10 \mathrm{cm}$
b $\ell=12 \mathrm{mm}, w=7 \mathrm{mm}, h=3 \mathrm{mm}$
c $\ell=18$ in., $w=9$ in., $h=9$ in
(FIGURE CAN NOT BE COPY)

Key Concepts

Right Rectangular Prism

A right rectangular prism is a three-dimensional shape that has six faces, each of which is a rectangle. All the interior angles in a right rectangular prism are 90 degrees, and opposite faces are congruent. This geometric solid is defined by its length, width, and height, which are used in various calculations such as finding its volume and surface area.

Total Surface Area

Total surface area is the sum of the areas of all the faces of a three-dimensional object. For a right rectangular prism, this involves calculating the area of each rectangular face and then summing these values. It is a key concept in geometry that helps in understanding how much material would be needed to cover the object completely.

Surface Area Formula

The surface area of a right rectangular prism can be calculated using the formula S = 2(lw + lh + wh), where 'l' represents length, 'w' represents width, and 'h' represents height. This formula works by adding the areas of the three distinct pairs of parallel faces and doubling the sum since each pair consists of two identical faces.

Units of Measurement

When dealing with problems involving surface area, it is important to consider the units of measurement provided for the dimensions. Consistent use of units is crucial for accurate calculations. In cases where different dimensions are given in various units, appropriate conversions must be carried out before applying the surface area formula.