math class 678 4-in-1 skill sheets
6.G.A.4 6th Grade Geometry

Nets & Surface Area

Represent three-dimensional figures using nets made of rectangles and triangles, and use the nets to find surface area.

How to explain it

At this standard, students represent rectangular and triangular prisms as nets, identify the rectangular and triangular faces, and use the nets to compute total surface area in mathematical and real-world problems.

The anchor students hold onto: To find surface area, identify every face of the solid, find the area of each face, then add them all up.

Where this leads next: 7th-grade geometry — scale drawings, area of circles, and surface area of more complex solids.

Worked examples

Example 1 Rectangular Prism
l=6, w=4, h=3 cm. Find SA.
Step 1Top/Bottom: 2(6x4) = 48
Step 2Front/Back: 2(6x3) = 36
Step 3Left/Right: 2(4x3) = 24
Step 4SA = 48 + 36 + 24 = 108 cm²
Answer108 cm²
Example 2 Triangular Prism
Legs 3 & 4 in (hyp 5); L=8.
Step 12 triangles: 2(1/2 x 3 x 4) = 12
Step 23 rects: (3+4+5) x 8 = 96
Step 3SA = 12 + 96 = 108 in²
Answer108 in²

Common mistakes

What students write Student counts only 5 faces for a rectangular prism (box), missing the hidden bottom face, leading to an SA that is too small by one face area.
The fix A rectangular prism ALWAYS has 6 faces — 3 congruent pairs (top/bottom, front/back, left/right). Use SA = 2lw + 2lh + 2wh to ensure all 3 pairs are counted.
What students write Student confuses volume and surface area, multiplying all 3 dimensions (V = l x w x h) to find "surface area," giving an answer in cubic units instead of square units.
The fix Surface area = sum of face AREAS (square units). Volume = 3D space inside (cubic units). For SA: find the area of each face, then add. Check: the answer must be in square units (cm², ft²).

Teacher tip

Head off the two predictable errors before they happen. First: A rectangular prism ALWAYS has 6 faces — 3 congruent pairs (top/bottom, front/back, left/right). Use SA = 2lw + 2lh + 2wh to ensure all 3 pairs are counted. Second: Surface area = sum of face AREAS (square units). Volume = 3D space inside (cubic units). For SA: find the area of each face, then add. Check: the answer must be in square units (cm², ft²).