a)
A(ABCD) = 144 } => 144 = AB² => AB = 12 cm
AB = BC
AB = 12 cm => AC = 12√2 cm
AM = MB } => MN = linie mijlocie in Δ ABC => MN = AB/2 = 6√2 cm
BN = NC
b)
MC = √MB² + BC² = √144 + 36 = √180 = 6√5 cm
A(MDC) = A(ABCD) - 2A(MBC)
= 144 - 2×12×6/2
= 72 cm²
Duc DP ⊥ MC
A(DMC) = 72 = MC×DP/2 =>
DP = 2×A(DMC)/MC = 2×144/6√5 cm = 24√5/5 cm
D'P = √DD'+ DP
= √(12)² + (24√5/5)²
= √144 + 576/5
= √720/5 + 576/5
= √1296/√5
= 36/√5
= 36√5/5 cm
