2026 NORTHBROOKS P1 Q8

The diagram shows a card which consists of a square \(PQRS\) of sides 10 cm and four identical isosceles triangles.

In triangle \(BQR\), \(BX\) is perpendicular to \(QR\) and \(BX=13\text{ cm}\).

The card is folded to form a right pyramid with \(PQRS\) as base and \(A,B,C,D\) meeting at the vertex.

Calculate

1. the height of the pyramid,[2]
2. the volume of the pyramid.[2]