math
posted by mhy .
a regular triangular pyramid with a slant height of 9 m has a volume equal to 50 m³. Find the lateral areas of the pyramid.

Answer is 81 square root of 3 sq.m

If the triangular base has area A and the pyramid has height h, the volume of the pyramid is 50 = 1/3 Ah so you have 150 = Ah and h=150/A. The area of the base is A=b^2*sqrt (3) /4 where b is the length of each side of the base.
So you have a h = 150 / (b^2*sqrt (3) /4) = 200sqrt (3) / b^2
The edge length e, slant heights, and base length b satisfy e^2 = h^2 + b^2 /3 and s^2 = h^2 +b^2 /12. e^2 s^2 = b^2 /4
Substituting into the equation s^2 = h^2 +b^2 /12 for h^2 = 120000b^4:
9^2 =120000 / b^4 +b^2 /12. This gives b = 6.26836.
Each of the three lateral triangles has an area BS /2 so the total lateral area of the pyramid is 3bs/2 = 3 (6.26836) (9) /2 = 84.62286.
You could find h using 9^2 = h^2 +6.26836^2 /12, then he = 8.81621.
Respond to this Question
Similar Questions

math/geometry
What are the surface areas of this two figures? 
geometry
How do you find the lateral area and perimeter of a pentagonal pyramid? 
Math
VWXYZ is a rectanglebased pyramid where WX = 66 cm and XY = 32 cm. The vertex is vertically above the center of the base. GIven that the slant heights of VA and VB are 56 cm and 63 cm respectively, find the total surfact area of the … 
geometry
A pyramid has a square base with each side measuring 105.5 meters. The slant height of the pyramid is 65.5 meters. Find the lateral surface area of the pyramid. 
Mathematics
OPQRS is a right pyramid whose base is a square of sides 12cm each. Given that the slant height of the pyramid is 15cm. Find the height of the pyramid, the volume of the pyramid, and the total surface area of the pyramid by first drawing … 
MATH
A regular triangular pyramid has an altitude of 9m and a volume of 46.8cu. meters. Find the length of the edges and the lateral area of the pyramid. 
Maths
OPQRS is a right pyramid whose base is a square of sides 12cm each. Given that the slant height of the pyramid is 15cm. Find the height of the pyramid. The volume of the pyramid and the total surface of the pyramid. 
Maths
OPQRS is a right pyramid whose base is a square of sides 12cm each. Given that the slant height of the pyramid is 15cm. Find the height of the pyramid. The volume of the pyramid and the total surface of the pyramid. 
Math
Regular triangular pyramid has the slant height k=12 cm and lateral area A = 198 cm2. Find the length of the base edge. 
math URGENT HELPPPP!
Regular triangular pyramid has the slant height k=12 cm and lateral area AL = 198 cm2. Find the length of the base edge.