MathDB

In prism

JHOPKINS

, quadrilaterals

JHOP

and

KINS

are parallel and congruent bases that are kites, where

JH = JP = KI = KS

and

OH = OP = NI = NS

; the longer two sides of each kite have length

\tfrac{4 + \sqrt{5}}{2}

, and the shorter two sides of each kite have length

\tfrac{5 + \sqrt{5}}{4}

. Assume that

\overline{JK}

\overline{HI}

\overline{ON}

, and

\overline{PS}

are congruent edges of

JHOPKINS

perpendicular to the planes containing

JHOP

and

KINS

. Vertex

J

is part of a regular pentagon

JAZZ'Y

that can be inscribed in prism

JHOPKINS

such that

A \in \overline{HI}

Z \in \overline{NI}

Z' \in \overline{NS}

Y \in \overline{PS}

AI = YS

, and

ZI = Z'S

. Compute the height of

JHOPKINS

(that is, the distance between the bases).

Problem Statement