An item of jewellery consists of two identical pyramids, PABCD and QABCD, joined at their common rectangular base. AB = 8mm, BC = 12mm and PQ = 30mm. The line pq passes through the centre of the rectangle ABCD.

Question

An item of jewellery consists of two identical pyramids, PABCD and QABCD, joined at their common rectangular base. AB = 8mm, BC = 12mm and PQ = 30mm. The line pq passes through the centre of the rectangle ABCD.

Calculate the area of triangle ABP
Calculate the area of triangle ADP

The item is to be dipped in silver at a cost of 0.4p per mm2

Calculate the cost of dipping

Answer 1

PQ is 4 units from AD and 6 units from AB. So,

The slant height of ∆ABP is √(15^2-6^2)

The slant height of ∆ADP is √(15^2-4^2)

Now you can easily figure each area, and then the cost.