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3 years ago

The base of a pyramid has n sides. Write an EXPRESSION for the number of faces of the pyramid.

2 answers:

3 0

<span>In general, if the pyramid has 'x' sides, then it will have 'x' lateral faces. Total Number of Faces = Number of Base Faces + Number of Lateral Faces. Total Number of Faces = 2 + x. So the formula is F=x%2B2 where "x" is the number of sides that the pyramid has and "F" is the total number of faces.</span>

Anvisha [2.4K]3 years ago

3 0

Answer: The expression for number of faces of a pyramid =1+n

Step-by-step explanation:

A Pyramid is a polyhedron or a three dimensional shape having a polygon base and all lateral faces are triangles .

Its base describe the number of other faces of it.

For example a triangular pyramid has a triangular base which gives rise to 3 lateral faces , and a rectangular pyramid has a rectangular base which give rise to 4 lateral faces and so on.....

So the total number of faces in a pyramid = base + lateral faces

If a pyramid has n sides therefore it give rise to n lateral faces such that

The total number of faces in a pyramid= 1+n .

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3 solutions:

$\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}}$

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is $tan(\frac{\theta}{2})$ so let's focus on that part of the equation first.

We know that:

$tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}$

therefore:

$cos(\frac{\theta}{2})\neq0$

so we need to find the angles that will make the cos function equal to zero. So we get:

$cos(\frac{\theta}{2})=0$

$\frac{\theta}{2}=cos^{-1}(0)$

$\frac{\theta}{2}=\frac{\pi}{2}+\pi n$

$\theta=\pi+2\pi n$

we can now start plugging values in for n:

$\theta=\pi+2\pi (0)=\pi$

if we plugged any value greater than 0, we would end up with an angle that is greater than $2\pi$ so, that's the only angle we cannot include in our answer set, so: