Surface area of prisms

Other applications of surface area

Sometimes you may come across prisms that have bases of different shapes, they could be a prism with 5 sides (pentagonal), 6 sides (hexagonal) or 7 sides (heptagonal). In working with these prisms, we take the same approach for calculating TSA, taking the sum of all of the individual faces.

Question 5

Hexa Chocs are investigating how much cardboard they require to cover the outside of a box, which is in the form of a hexagonal prism, for their finest dark chocolate range. Find the amount of cardboard needed for each box.

The hexagonal cross-section of the prism has area 43 cm².
Each side of the hexagonal cross-section has length 5 cm.
The length of the prism is 21 cm.

Solution

The surface area of each hexagonal face is 43 cm².
There are two of these faces, so we have 2 × 43 cm² = 86 cm².

The other 6 faces of the hexagonal prism are rectangles each with width 5 cm and length 21 cm.

A	= 21 × 5 × 6
	= 630 cm²
Therefore the TSA of the hexagonal prism	= 86 cm² + 630 cm²
	= 716 cm²

Therefore the amount of cardboard required to construct a hexagonal prism with these dimensions is 716 cm².

Question 4