Could someone help me with this?

Question

A tetrahedron (not rectangular) has vertices at A, B, C, and D. The length of the altitude from A to the base (△BCD) measures 6 in. It is given that m∠BCD = 90°,

 BC = 4 in.,

 and CD = 9 in.

A tetrahedron has the following four triangular faces: △A B D, △A C D, △A B C, and △B C D. ∠C of △B C D is labeled as a right angle.

(a)

Find the volume (in cubic inches) of the pyramid.

 in³

(b)

Find the length (in inches) of the altitude from vertex D to the base (△ABC); note that A_ABC = 12 in².

Answer 1

(a) Area A_ΔABC= BC·CD/2 = 4cm·9cm/2 = 18 cm²; So volume V = 18cm²·6cm/3 = 36 cm³.

(b) Now let altitude from vertex D is h_D, then V = A_ΔABC·h_D/3, from here h_D = 3V/A_ΔABC = 3·36cm³/12cm² =

9 cm