Question

Find the area of hexagon PQRSTU in which QN is perpendicular to PS, RL is perpendicular to PS, TM is perpendicular to PS, UO is perpendicular to PS such that PO= 4m, ON=2m, NM= 6m, ML=2m, LS= 6m, UO= 6m, TM= 8m, QN= 2m, RL=4m.

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Answer 1

Area of the hexagon PQRSTU = Area of ΔPQN + Area of quad QRLN + Area of ΔRSL + Area of ΔTMS + Area of quad OMTU + Area of ΔPOU

= ( $\frac{1}{2}$ * PN * QN) + ( $\frac{1}{2}$ * (RL + QN) * NL) + ( $\frac{1}{2}$ * LS * RL) + ( $\frac{1}{2}$ * MS * TM) +

( $\frac{1}{2}$ * (TM + UO) * OM) + ( $\frac{1}{2}$ * PO * UO)

= ( $\frac{1}{2}$ * 6 * 2) + ( $\frac{1}{2}$ * (4 + 2) * 8) + ( $\frac{1}{2}$ * 6 * 4) + ( $\frac{1}{2}$ * 8 * 8) +

( $\frac{1}{2}$ * (8 + 6) * 8) + ( $\frac{1}{2}$ * 4 * 6)

= 6 + 24 + 12 + 32 + 56 + 12

=142 $m^2$.