🎓 Mini-Lesson: What is Surface Area?
Surface Area = The total area of ALL the faces added together
Think of it like wrapping a present - how much wrapping paper do you need to cover the whole box?
🧊 Surface Area of a CUBE
What is a cube? A cube has 6 faces that are all identical squares.
Net of a cube (unfolded):
Top
Left
Front
Right
Back
Bottom
6 identical square faces
📐 Formula for CUBE
Surface Area = 6 × (side × side)
or
Surface Area = 6 × side²
Example: Find the surface area of a cube with side length 4cm
Step 1: Find the area of ONE face
Area of one face = 4 × 4 = 16 cm²
Area of one face = 4 × 4 = 16 cm²
Step 2: Multiply by 6 (because there are 6 faces)
Surface Area = 6 × 16 = 96 cm²
Surface Area = 6 × 16 = 96 cm²
📦 Surface Area of a CUBOID
What is a cuboid? A cuboid has 6 rectangular faces. Opposite faces are identical.
A cuboid has:
- Length (l)
- Width (w)
- Height (h)
The 6 faces are:
- Top and Bottom (2 faces: l × w each)
- Front and Back (2 faces: l × h each)
- Left and Right (2 faces: w × h each)
📐 Formula for CUBOID
Surface Area = 2(lw + lh + wh)
This means: 2 × (length×width + length×height + width×height)
Example: Find the surface area of a cuboid: length=5cm, width=3cm, height=4cm
Step 1: Calculate lw (top and bottom)
lw = 5 × 3 = 15 cm²
Two faces = 2 × 15 = 30 cm²
lw = 5 × 3 = 15 cm²
Two faces = 2 × 15 = 30 cm²
Step 2: Calculate lh (front and back)
lh = 5 × 4 = 20 cm²
Two faces = 2 × 20 = 40 cm²
lh = 5 × 4 = 20 cm²
Two faces = 2 × 20 = 40 cm²
Step 3: Calculate wh (left and right)
wh = 3 × 4 = 12 cm²
Two faces = 2 × 12 = 24 cm²
wh = 3 × 4 = 12 cm²
Two faces = 2 × 12 = 24 cm²
Step 4: Add them all together
Surface Area = 30 + 40 + 24 = 94 cm²
Surface Area = 30 + 40 + 24 = 94 cm²
💡 Remember:
- Surface area is always in square units (cm², m², etc.)
- A cube is a special cuboid where l = w = h
- Always check you've counted all 6 faces!
✏️ Practice Questions
Calculate the surface area. Remember to include units (cm²)!