Skill: Find surface area using nets

A net shows all the faces of a solid unfolded into one flat shape. To find the surface area, find the area of each face and add the areas together. Use square units because area measures the amount of surface covered.

Example

A net forms a rectangular prism with:

• length: $5$ units
• width: $3$ units
• height: $2$ units

Step 1: Identify the faces

A rectangular prism has three pairs of matching, or congruent, rectangles:

• $2$ rectangles measuring $5 \times 3$
• $2$ rectangles measuring $5 \times 2$
• $2$ rectangles measuring $3 \times 2$

The net shows these six faces unfolded.

Step 2: Find the area of each type of face

Use the area formula for a rectangle:

$$\text{Area}=\text{length}\times\text{width}$$

For the $5 \times 3$ faces:

$$5\times3=15$$

Since there are two:

$$2\times15=30$$

For the $5 \times 2$ faces:

$$5\times2=10$$

Since there are two:

$$2\times10=20$$

For the $3 \times 2$ faces:

$$3\times2=6$$

Since there are two:

$$2\times6=12$$

Step 3: Add the areas

$$30+20+12=62$$

The surface area of the rectangular prism is:

$$\boxed{62\text{ square units}}$$

Remember: surface area includes the areas of all the exposed faces in the net. It measures the outside covering of the solid, not the space inside it.