MathDB

The rectangle

ABCD

below has dimensions

AB = 12 \sqrt{3}

and

BC = 13 \sqrt{3}

. Diagonals

\overline{AC}

and

\overline{BD}

intersect at

P

. If triangle

ABP

is cut out and removed, edges

\overline{AP}

and

\overline{BP}

are joined, and the figure is then creased along segments

\overline{CP}

and

\overline{DP}

, we obtain a triangular pyramid, all four of whose faces are isosceles triangles. Find the volume of this pyramid.
[asy] pair D=origin, A=(13,0), B=(13,12), C=(0,12), P=(6.5, 6); draw(B--C--P--D--C^^D--A); filldraw(A--P--B--cycle, gray, black); label("

A

", A, SE); label("

B

", B, NE); label("

C

", C, NW); label("

D

", D, SW); label("

P

", P, N); label("

13\sqrt{3}

", A--D, S); label("

12\sqrt{3}

", A--B, E);[/asy]

Problem Statement