Question

Find the SA of this pyramid 4 slant and 5 wide base rectangle

Answer 1

I need one clarification: is the base a square 5 × 5, or a rectangle 5 × (some other length)? And does the slant height 4 apply to all triangular faces (i.e., a right regular pyramid)?

If it is a square base 5 × 5 and the slant height is 4 for each triangular face, then:

- Base area = 5·5 = 25
- Area of one triangular face = (1/2)·base side·slant height = (1/2)·5·4 = 10
- There are 4 faces, so lateral area = 4·10 = 40
- Total surface area = base + lateral = 25 + 40 = 65

So SA = 65 square units.

If the base is a rectangle a × b, the total surface area is
SA = ab + (1/2)(a·s_a + b·s_b),
where s_a and s_b are the slant heights of the triangular faces on sides of length a and b. For a right pyramid with apex over the center and vertical height h,
s_a = sqrt(h^2 + (b/2)^2), s_b = sqrt(h^2 + (a/2)^2).

Tell me whether the base is 5×5 or give the other base side (or the pyramid height) and I’ll finish the computation.