SME
Grade 6 Math · Geometry
Surface area and volume
Use this for “Find the surface area of a box 5 cm long, 3 cm wide and 2 cm tall.”
Diagram
Six faces add to 62 cm².
This is an example. Type your own values to start a new problem.
Length
example
Width
example
Height
example
Area of top and bottom
worked out (not typed)
Area of front and back
worked out (not typed)
Area of the two ends
worked out (not typed)
Surface area
worked out (not typed)
Formulas
2 × (5 × 3) = 30
2 × (length × width) = area of top and bottom
2 × (5 × 2) = 20
2 × (length × height) = area of front and back
2 × (3 × 2) = 12
2 × (width × height) = area of the two ends
30 + 20 + 12 = 62
Areas of top and bottom + front and back + two ends = surface area
Assumptions
•
Surface area is the area of every face added together.
•
A box has three pairs of matching faces.
•
Area is in square units.
Step-by-step
WE KNOW
Length: 5 cm
Width: 3 cm
Height: 2 cm
FIND
area of top and bottom, area of front and back, area of the two ends, surface area
Step 1 · Find area of top and bottom
2 × (5 × 3) = ?
2 × (length × width) = area of top and bottom
The top and bottom are length by width: two of them.
Area of top and bottom = 30 cm²
Step 2 · Find area of front and back
2 × (5 × 2) = ?
2 × (length × height) = area of front and back
The front and back are length by height: two of them.
Area of front and back = 20 cm²
Step 3 · Find area of the two ends
2 × (3 × 2) = ?
2 × (width × height) = area of the two ends
The two ends are width by height: two of them.
Area of the two ends = 12 cm²
Step 4 · Find surface area
30 + 20 + 12 = ?
Areas of top and bottom + front and back + two ends = surface area
Add the areas of all six faces.
Surface area = 62 cm²
Check
Put the numbers back in. Both sides should match.
2 × (5 × 3) = 30 ✓
2 × (5 × 2) = 20 ✓
2 × (3 × 2) = 12 ✓
30 + 20 + 12 = 62 ✓
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