If a square and a rhombus stand on the same base, then what would be the ratio of the area of square and rhombus?

Question

A certain right pyramid with a square base has the same numerical surface area as its volume. If it is also the only right pyramid with a square base to have that certain surface area and volume, what is its height?

Answer 1

Let the base of square and rhombus be a units . Square all sides equal ;;; Area of square=a^2;;

let the height of rhombus , i.e perpendicular distance from the top edge to the base be h units and included angle be x

then area of rhombus =a*h=a^2sinx

ratio = (a^2)/(a^2*sinx) === 1/sinx and since 0<x<90 ;; 0<sinx<1;;; the ratio will always be greater than 1 ,,,,