Surface area and volume — prisms and cylinders

Before we dive into calculations, let's make sure we understand the shapes we're working with.

Think of a prism like a loaf of bread — every slice you cut has the same shape. Common prisms include:

• Rectangular prisms (boxes) — bases are rectangles
• Triangular prisms (like Toblerone boxes) — bases are triangles
• Pentagonal prisms, hexagonal prisms, etc.

Think of a can of soup or a paper towel roll — these are everyday cylinders. Although a cylinder is not technically a prism (because its base is a circle, not a polygon, and its lateral surface is curved), it shares the same elegant volume and surface area logic as prisms, so we study them together.

Imagine you want to wrap a gift box in paper. The amount of wrapping paper needed equals the surface area of the box.

Surface area is always measured in square units — such as ${\text{cm}}^2$, ${\text{m}}^2$, or ${\text{mm}}^2$.

To find the surface area of any prism or cylinder, we use the same general strategy:

1. Identify all the faces of the shape
2. Calculate the area of each face
3. Add them all together