Regular triangular pyramid has the slant height k=12 cm and lateral area AL = 198 cm2. Find the length of the base edge.
With a slant height of 12, each triangular face has a base of s and a height of 12, so
3(12s/2) = 198
s = 11
that makes no sense
To find the length of the base edge of a regular triangular pyramid, we need to use the formula for the lateral area of a regular triangular pyramid, which is given by:
AL = (1/2) × perimeter of the base × slant height
In this case, we are given the slant height (k = 12 cm) and the lateral area (AL = 198 cm²). We need to find the length of the base edge, which we'll denote as "s".
First, let's find the perimeter of the base. A regular triangular pyramid has a triangular base, and the perimeter of a triangle is given by the sum of its three side lengths. However, since it is regular, all the sides are the same length.
Let's assume the length of each side of the base is "s". Since it's a regular triangle, all three sides have length "s". Therefore, the perimeter of the base would be 3s.
Now, let's substitute the values into the formula for the lateral area and solve for s:
AL = (1/2) × 3s × k
198 = (1/2) × 3s × 12
198 = (3/2) × s × 12
198 = 3s × 6
198 = 18s
To find the value of s, divide both sides of the equation by 18:
s = 198 / 18
s = 11 cm
Therefore, the length of the base edge is 11 cm.