Question

A regular triangular pyramid with a slant height of 9 m has a volume equal to 50 m^3. find the lateral area of the pyramid

Answer 1

we are given a regular triangular pyramid with a slant height of 9 m and volume of 50 m3. We can get the altitude of the pyramid by sin 60 = h / 9; h is equal to 7.7942 m. Volume is equal to 1/3 h * B, B is equal to 19.2451 m2. perimeter of the base is 3*9 m equal to 27 meters. The lateral area has  a formula of 1/2 pl, substituting, lateral area is equal to 121.5 m2.