MATHEMATICS · Multi-part · IB Diploma Programme · Mathematics: Analysis and Approaches · Geometry and Trigonometry · Geometry and Trigonometry
Problem
A square-based pyramid has coordinates A(4,0,2), B(−1,3,2), C(1,−5,2), and D. The apex lies directly above the centre of the base, and the pyramid has surface area 210 units2.
(1) Find the coordinates of D .
(2) Find the height of the pyramid, correct to 1 decimal place.
(3) Hence find the volume of the pyramid.