Find the height in a regular quadrangular pyramid if the apothem is 5 cm and the side rib is 34 cm.

Given:

SABCD – pyramid

AB = BC

SH – pyramid height

SK – apothema

SK – 5 cm

SC – rib

SC – root of 34 cm

Find: SH

Solution: Triangle SKC is rectangular. CK ^ 2 = SC ^ 2 – sK ^ 2 = 34 – 25 = 9;

triangle CKH – isosceles and right-angled HK = CK;

triangle SHK – rectangular, SH ^ 2 = SK ^ 2 – HK ^ 2 = 25 – 9 = 16;

SH = 4 cm.

Answer: 4 cm.