Regular triangular pyramid has 6 cm long base edge and slant height k=9 cm. Find the lateral area of the pyramid.
and
Regular triangular pyramid has the slant height k=12 cm and lateral area AL = 198 cm2. Find the length of the base edge.
81 cm
To find the lateral area of a regular triangular pyramid, we need either the base edge length and slant height, or the slant height and lateral area. Let's solve each problem step by step.
1. Regular triangular pyramid with a 6 cm base edge and a slant height of 9 cm:
The lateral area (LA) of a regular triangular pyramid can be calculated using the formula:
LA = (1/2) × perimeter of the base × slant height
To find the perimeter of the base, we need to know the length of one side. Since it's a regular triangular pyramid, all sides of the base are equal.
Given the base edge length of 6 cm, we can calculate the perimeter:
Perimeter = base edge + base edge + base edge = 6 cm + 6 cm + 6 cm = 18 cm
Now, we can find the lateral area:
LA = (1/2) × 18 cm × 9 cm = 81 cm²
Therefore, the lateral area of the regular triangular pyramid is 81 cm².
2. Regular triangular pyramid with a slant height of 12 cm and a lateral area of 198 cm²:
Using the formula for the lateral area:
LA = (1/2) × perimeter of the base × slant height
We can rearrange the formula to find the perimeter of the base:
Perimeter = (2 × LA) / slant height
Given a slant height of 12 cm and a lateral area of 198 cm², we can calculate the perimeter of the base:
Perimeter = (2 × 198 cm²) / 12 cm = 33 cm
Since it's a regular triangular pyramid, the perimeter of the base is also equal to three times the length of one side:
Perimeter = 3 × side length
Therefore, the length of one side of the base (base edge length) is:
base edge length = Perimeter / 3 = 33 cm / 3 = 11 cm
Thus, the length of the base edge of the regular triangular pyramid is 11 cm.
thanks isabella
no problemo
the area is three triangles, each with base 6 and height 9.
Recall that the area of a triangle is A = 1/2 bh
and
same problem, only this time, solve for b