Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Ta có: \(AM=\frac12\times AB\)
=>\(S_{DMA}=\frac12\times S_{DAB}\)
Ta có: \(AQ=\frac12\times AD\)
=>\(S_{AMQ}=\frac12\times S_{ADM}=\frac14\times S_{ADB}\)
Ta có: \(CN=\frac12\times CB\)
=>\(S_{DNC}=\frac12\times S_{DBC}\)
Ta có: \(CP=\frac12\times CD\)
=>\(S_{PCN}=\frac12\times S_{DNC}=\frac12\times\frac12\times S_{DBC}=\frac14\times S_{DBC}\)
Ta có: \(BN=\frac12\times BC\)
=>\(S_{ABN}=\frac12\times S_{ABC}\)
Ta có: \(BM=\frac12\times BA\)
=>\(S_{BMN}=\frac12\times S_{BMC}=\frac14\times S_{ABC}\)
Ta có: \(DP=\frac12\times DC\)
=>\(S_{DAP}=\frac12\times S_{DAC}\)
\(DQ=\frac12\times DA\)
=>\(S_{DQP}=\frac12\times S_{DPA}=\frac12\times\frac12\times S_{DAC}=\frac14\times S_{DAC}\)
Ta có: \(S_{AMQ}+S_{BMN}+S_{CNP}+S_{DQP}+S_{MNPQ}=S_{ABCD}\)
=>\(S_{MNPQ}+\frac14\times\left(S_{ABC}+S_{ADC}\right)+\frac14\times\left(S_{ABD}+S_{CBD}\right)=S_{ABCD}\)
=>\(S_{MNPQ}=\frac12\times S_{ABCD}=\frac12\times100=50\left(\operatorname{cm}^2\right)\)
Ta có: \(ME=\frac12\times MN\)
=>\(S_{QEM}=\frac12\times S_{QMN}\)
Ta có: \(MH=\frac12\times MQ\)
=>\(S_{MHE}=\frac12\times S_{QME}=\frac14\times S_{MQN}\)
Ta có: \(PG=\frac12\times PQ\)
=>\(S_{NGP}=\frac12\times S_{NPQ}\)
Ta có: \(PF=\frac12\times PN\)
=>\(S_{PGF}=\frac12\times S_{PGN}=\frac14\times S_{PQN}\)
Ta có: \(QH=\frac12\times QM\)
=>\(S_{QHP}=\frac12\times S_{QMP}\)
Ta có: \(QG=\frac12\times QP\)
=>\(S_{GHQ}=\frac12\times S_{QHP}=\frac14\times S_{QMP}\)
Ta có: \(NE=\frac12\times NM\)
=>\(S_{PEN}=\frac12\times S_{PMN}\)
Ta có: \(NF=\frac12\times NP\)
=>\(S_{NFE}=\frac12\times S_{NEP}=\frac12\times\frac12\times S_{NMP}=\frac14\times S_{NMP}\)
Ta có: \(S_{NFE}+S_{MHE}+S_{QHG}+S_{PGF}+S_{EHGF}=S_{MNPQ}\)
=>\(S_{EHGF}=S_{MNPQ}-\frac14\times\left(S_{MQN}+S_{PQN}\right)-\frac14\times\left(S_{NMP}+S_{QMP}\right)\)
=>\(S_{EHGF}=S_{MNPQ}-\frac14\times S_{MNPQ}-\frac14\times S_{MNPQ}=\frac12\times S_{MNPQ}\)
\(=\frac12\times50=25\left(\operatorname{cm}^2\right)\)