Square Pyramid
Go to Surface Area or Volume.
Square Pyramid Facts
Notice these interesting things:
- It has 5 Faces
- The 4 Side Faces are Triangles
- The Base is a Square
- It has 5 Vertices (corner points)
- It has 8 Edges
Surface Area
When side faces are the same:
Surface Area = [Base Area] + 1 2 × Perimeter × [Slant Length]
Example: Side faces are the same, slant length is 3, base is square with side length of 5
Surface Area = [Base Area] + ½ × Perimeter × [Slant Length]
= [5 × 5] + ½ × (5+5+5+5) × 3
= 25 + ½ × 20 × 3
= 25 + 30
= 55
When side faces are different we can calculate the area of the base and each triangular face separately and then add them up.
Volume
Volume = 1 3 × [Base Area] × Height
Example: base is square with side length of 5 , height is 6
Volume=
1
3
× [Base Area] × Height
=
1
3
× [5 × 5] × 6
=
1
3
× 150
= 50
Play with it here. Note how the formula stays the same when it "leans over" (oblique):
Other Images
1864, 1865, 1866, 1867