a right VEFGH with a square base of 8cm and a slant edge of 20cm. Points A, B, C and D lie on the slant edges of the pyramid such that VA =VB = VC = VD =10cm and plane ABCD is parallel to the base EFGH.
(a) Find the length of AB.
(b) Calculate, correct to 2 decimal places:
(i) the length of AC;
(ii) the perpendicular height of the pyramid VABCD.
(c) The pyramid VABCD was cut off. Find the volume of the frustum ABCDEFGH correct to 2 decimal places.
I assume you mean a right pyramid VEFGH, with base EFGH.
A,B,C,D are the midpoints of the slant edges.
Drop an altitude from V to M, the center of the base.
Let N be the midpoint of EF.
Then MN = EN = 4, and ME = 4√2
That means that the altitude MV^2 + ME^2 = 20^2, and MV = 4√23
So, AB is 1/2 (EF) = 4
ABCD is a square of side 4
volume of VABCD = 1/8 volume VEFGH
You should be able to answer the questions now.