Question

Question is in picture below

Answer 1

`find \: lengh \: bc \: because \: find \: the \: base \: area \: \\ bc = ad \\ from \: ac = 15mm \\ ab = 12mm \\ from Pythagoras \: {c}^(2) = {a}^(2) + {b}^(2) \\ is \: {(ac)}^(2) = {(bc)}^(2) + {(ab)}^(2) \\ 15 ^(2) = {(bc)}^(2) + {12}^(2) \\ {(bc)}^(2) = 15^(2) - {12}^(2) \\ bc = \sqrt{{15}^(2) - {12}^(2) } \\ bc = √(225 - 144) \\ bc = √(81) \\ bc = 9 \: or \: - 9 \\ bc = 9 \\ base \: area \: = bc \: * \: ab \\ = 9 * 12 = 108 {mm}^(2) \\ volume \: pyramid \: = \: (1)/(3) * base \: area * hight \\ = (1)/(3) * 108 {mm}^(2) * 13mm \\ = 468 {mm}^(3)`