Determine the slant height of a right pyramid whose lateral area is 90 ft^2 and whose base is a regular hexagon with a 3 ft side.
The lateral area of a pyramid can be calculated by the following formula:
Area, A = pa/2
p=permimeter of the base polygon
a=apothem of the pyramid, i.e. the slant height.
Therefore, the slant height (or the apothem, a) can be calculated as follows:
a = 2*lateral area/perimeter of base
= 2A/p
How do I find the perimeter of base
is it 18
Yes, 18 is correct.
A hexagon has 6 sides, each of length 3 ft. So
Perimeter, p = 6*3 ft = 18 ft.
so whats the answer
The answer is 10
To determine the slant height of a right pyramid, you can use the formula for lateral area, the formula for the area of a regular hexagon, and the formula for the lateral surface area of a pyramid.
First, let's find the lateral surface area of the pyramid using the given lateral area of 90 ft². The lateral surface area (LA) of a pyramid is given by the formula:
LA = (1/2) × Perimeter of Base × Slant Height
We are given that the lateral area is 90 ft², and the base is a regular hexagon with a side length of 3 ft. The perimeter of a regular hexagon is given by the formula:
Perimeter of Hexagon = 6 × Side Length
So, the perimeter of the hexagon base is:
Perimeter of Hexagon = 6 × 3 = 18 ft
Plugging in the values into the formula for the lateral surface area:
90 = (1/2) × 18 × Slant Height
To isolate the slant height, divide both sides of the equation by (1/2) × 18:
90 / (1/2) × 18 = Slant Height
90 / 9 = Slant Height
10 = Slant Height
Therefore, the slant height of the right pyramid is 10 ft.