Question

A regular square-based pyramid has a surface area of 33 m2. If its triangular faces have an area of 6 m2, what is the length of the base of the pyramid?

Answer 1

Answer:

First we can do 33 time 6

Step-by-step explanation:

Answer 2

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

$A = \frac{1}{2}(b)(h)$

⇒ $6 = \frac{1}{2}(b)(h)$

⇒ $6(2) = (b)(h)$

⇒ $12 = (b)(h)$

The formula of surface area of square pyramid is

$SA = b^{2}+2bh$

⇒ $33=b^{2} +2(12)$

⇒ $33-24=b^{2}$

⇒ $b=\sqrt{9}$

⇒ $b=3$

Hence we can conclude that the length of the base of the pyramid is 3 meters.

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