Surface area of general prisms

Remember that:

The surface area of a prism is the sum of the areas of each face.

Example 4

Find the surface area of the prism pictured.

Solution

Here we can see that we have six faces.

Detailed description

\begin{align}\text{Area of base rectangle} &= 10 × 30\\ &= 300\ \text{cm²}\\ \text{Area of top rectangle} &= 8 × 30\\ &= 240\ \text{cm²}\\ \text{Area of rectangular side faces} &= 2 × 3.2 × 30\\ &= 192\ \text{cm²}\\ \text{Area of trapezium faces} &= 2 × \dfrac{1}{2} × 3 × (8 + 10)\\ &= 54\ \text{cm²}\\ \text{Surface area} &= 300 + 240 + 192 + 54\\ &= 786\ \text{cm²}\end{align}