SME
Grade 6 Math · Problem type
Surface area of pyramids
Use this for “Find the surface area of the square pyramid from its net.”
Diagram
Base and four triangles add to 96 cm².
This is an example. Type your own values to start a new problem.
Base side
example
Triangle height
example
Base area
worked out (not typed)
Area of one triangle
worked out (not typed)
Surface area
worked out (not typed)
Formulas
6 × 6 = 36
Base side × base side = base area
1
2
×
6
×
5
=
15
Half of base side × triangle height = area of one triangle
36 + 4 × 15 = 96
Base area + 4 × area of one triangle = surface area
Assumptions
•
The net is a square base and 4 matching triangles.
•
Each triangle’s height is measured on its face, from the base edge to the top.
•
The triangles must be tall enough to meet at the top: more than half the base side.
•
Area is in square units.
Step-by-step
WE KNOW
Base side: 6 cm
Triangle height: 5 cm
FIND
base area, area of one triangle, surface area
Step 1 · Find base area
6 × 6 = ?
Base side × base side = base area
The base is a square.
Base area = 36 cm²
Step 2 · Find area of one triangle
1
2
×
6
×
5
=
?
Half of base side × triangle height = area of one triangle
Each face is a triangle on a base side: half of base × height.
Area of one triangle = 15 cm²
Step 3 · Find surface area
36 + 4 × 15 = ?
Base area + 4 × area of one triangle = surface area
Add the square base and the four matching triangles.
4 × 15 = 60
36 + 60 = 96
Surface area = 96 cm²
Check
Put the numbers back in. Both sides should match.
6 × 6 = 36 ✓
1
2
×
6
×
5
=
15
✓
36 + 4 × 15 = 96 ✓
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Surface area and volume of cubes
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Volume of prisms with fractional edges
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