Respuesta :
The length of the base of the pyramid is 3 meters.
What is a square pyramid?
A pyramid is a polyhedron that has a base and 3 or greater triangular faces that meet at a point above the base. A square pyramid is a pyramid with a square base, four triangular sides, five vertices, and eight edges.
For the given situation,
The surface area of the pyramid = 33 m^2
Area of triangular faces = 6 m^2
Let the base of the pyramid be b and the height be h.
The formula of area of triangle is
[tex]A = \frac{1}{2}(b)(h)[/tex]
⇒ [tex]6 = \frac{1}{2}(b)(h)[/tex]
⇒ [tex]6(2) = (b)(h)[/tex]
⇒ [tex]12 = (b)(h)[/tex]
The formula of surface area of square pyramid is
[tex]SA = b^{2}+2bh[/tex]
⇒ [tex]33=b^{2} +2(12)[/tex]
⇒ [tex]33-24=b^{2}[/tex]
⇒ [tex]b=\sqrt{9}[/tex]
⇒ [tex]b=3[/tex]
Hence we can conclude that the length of the base of the pyramid is 3 meters.
Learn more about square pyramid here
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