Surface Area & Nets • Topic 2 of 2

Calculating Total Surface Area from Net

What is Surface Area?

Surface area is the total area of all faces of a 3D shape. It's like the amount of wrapping paper needed to cover the entire shape.

Method 1: Using a Net

Draw or visualize the net
Find area of each face
Add all areas together

Method 2: Using a Formula

Shape	Surface Area Formula
Rectangular Prism	SA = 2(lw + lh + wh)
Cube	SA = 6s²
Triangular Prism	SA = bh + 2ls + lw (varies)
Square Pyramid	SA = s² + 2sl

Note: "l" = length, "w" = width, "h" = height, "s" = side

SURFACE AREA FROM NET - RECTANGULAR PRISM:

    Dimensions: l=6 cm, w=4 cm, h=3 cm
    
    Net with labeled faces:
    
                    ┌─────────┐
                    │  Top    │
                    │ 6 × 4   │ = 24 cm²
    ┌─────────┬─────┼─────────┼─────┬─────────┐
    │  Left   │Front│ Bottom  │Back │  Right  │
    │ 3 × 4   │6×3  │ 6 × 4   │6×3  │ 3 × 4   │
    │ =12 cm² │=18  │ =24 cm² │=18  │ =12 cm² │
    └─────────┴─────┴─────────┴─────┴─────────┘
    
    Total SA = 12 + 18 + 24 + 24 + 18 + 12 = 108 cm²
    
    Formula check: SA = 2(6×4 + 6×3 + 4×3)
                  = 2(24 + 18 + 12) = 2×54 = 108 ✓


SURFACE AREA FROM NET - CUBE:

    Side s = 5 cm
    
    Each square face: 5×5 = 25 cm²
    6 faces × 25 = 150 cm²
    
    Formula: SA = 6s² = 6×25 = 150 cm²


SURFACE AREA FROM NET - TRIANGULAR PRISM:

    Triangle base b=4 cm, height h=3 cm
    Prism length L=10 cm
    
    Faces:
    - Triangle 1: ½×4×3 = 6 cm²
    - Triangle 2: 6 cm²
    - Rectangle 1 (bottom): 4×10 = 40 cm²
    - Rectangle 2 (side 5 cm): 5×10 = 50 cm²
    - Rectangle 3 (other side 5 cm): 50 cm²
    
    Total SA = 6 + 6 + 40 + 50 + 50 = 152 cm²

Solved Examples

Worked Example

Find the surface area of a rectangular prism with dimensions 8 cm, 5 cm, and 3 cm.

Solution (Formula):

SA = 2(lw + lh + wh)
SA = 2(8×5 + 8×3 + 5×3)
SA = 2(40 + 24 + 15)
SA = 2 × 79 = 158
Answer: 158 cm²

Solution

Worked Example

A cube has side length 7 cm. Find its surface area.

Solution

SA = 6s² = 6 × 7² = 6 × 49 = 294
Answer: 294 cm²

Worked Example

A triangular prism has triangular base with base 6 cm and height 4 cm. The prism length is 12 cm. The other two sides of triangle are 5 cm each. Find SA.

Solution

Triangle area = ½×6×4 = 12 cm² (×2 = 24 cm² for both)
Bottom rectangle: 6×12 = 72 cm²
Side rectangles: 5×12 = 60 cm² each (×2 = 120 cm²)
Total SA = 24 + 72 + 120 = 216
Answer: 216 cm²

Key Points

Surface area = sum of areas of all faces
Use net to visualize all faces
Be careful not to miss any faces
Opposite faces have equal area
Use formulas to save time

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.Total surface area is the sum of the areas of all:

Explanation: All faces.

Q2.The TSA of a cube is:

Explanation: $6a^2$.

Q3.The TSA of a cuboid is:

Explanation: $2(lb+bh+hl)$.

Q4.Surface area is measured in:

Explanation: Square units.

Practice more MCQs → 📝 Assignment · 35 marks