The lateral area of a regular pyramid is 300 square units. The perimeter of its base is 100 units. Find the slant height of the pyramid.

my answer is 5 units is this correct?

To find the slant height of a regular pyramid, we'll need to use some formulas and calculations.

A regular pyramid has a base that is a regular polygon, and all of its faces are triangles.

First, let's calculate the base length of the regular pyramid using the given perimeter.

The perimeter of the base is 100 units, and since the base is a regular polygon, we can divide the perimeter by the number of sides to find the length of each side.

Since we don't know the number of sides, let's assume the base is an n-sided polygon. So each side of the base has a length of 100/n units.

Next, let's calculate the area of the base. For a regular n-sided polygon, the formula for the area is A = (n × s²)/(4 × tan(π/n)), where s is the side length.

Since we know the lateral area of the pyramid is 300 square units, we can set up an equation:

300 = (n × s × l)/2,

where l is the slant height. Rearranging, we get:

600 = n × s × l.

Now, let's substitute the base length we calculated earlier into the equation:

600 = n × (100/n) × l.

Simplifying, we find:

600 = 100l.

Dividing both sides by 100, we get:

6 = l.

Therefore, the slant height of the pyramid is 6 units, not 5 units.

So, your answer of 5 units is incorrect. The correct slant height is 6 units.

Not quite!

The lateral area of a pyramid, A
=(1/2)(base-perimeter)* slant height

So given A=300, base perimeter =100
we have
slant height = A*2/base-perimeter=6 units