E F4. Find the area of hexagon ABCDEF in which BL 1 AD, CM IAD,EN I AD and FP AD such that AP = 6 cm, PL = 2 cm,LN = 8 cm. NM = 2 cm, MD = 3 cm, FP = 8 cm, EN = 12 cm.BL = 8 cm and CM = 6 cm.ASMNBO

E F4. Find the area of hexagon ABCDEF in which BL 1 AD, CM IAD,EN I

1.	E F4. Find the area of hexagon ABCDEF in which BL 1 AD, CM IAD,EN I AD and FP AD such that AP = 6 cm, PL = 2 cm,LN = 8 cm. NM = 2 cm, MD = 3 cm, FP = 8 cm, EN = 12 cm.BL = 8 cm and CM = 6 cm.ASMNBO
Answer» The GIVEN details are,BL⊥AD, CM⊥AD, EN⊥AD and FP⊥AD $$AP=6 cm, PL= 2 cm, LN=8 cm, NM=2 cm, MD=3 cm, FP=8 cm, EN=12 cm. BL= 8 cm , CM=6cm.AL=AP+PL=6+2=8cmPN=PL+LN=2+8=10cmLM=LN+NM=8+2=10cmND=NM+MD=2+3=5cmBy Using the formula,Area (hex. ABCDEF) =area(△APF)+area(△DEN)+area(△ABL)+area(△CMD)+area(Trap.PNEF)+area(Trap.LMCB)Area of triangle =1/2×base×heightArea of TRAPEZIUM =1/2×(sum of PARALLEL sides)×height∴lets calculate,Area(△APF)=1/2(AP)×(FP)=1/2×6×8=24cm 2 Area(△DEN)=1/2(ND)×(EN)=1/2×5×12=30cm 2 Area(△ABL)=1/2(AL)×(BL)=1/2×8×8=32cm 2 Area(△CMD)=1/2(MD)×(CM)=1/2×3×6=9cm 2 Area(Trap.DMNE)=1/2×(FP+EN)×ON=1/2×(18+12)×1=100cm 2 Area(Trap.DMNE)=1/2×(BL+CM)×LM=1/2×(BL+CM)×LM=1/2×(8+6)×10=70cm 2 ∴Area(her.ABCDEF)=area(△APF)+area(△DEN)+area(△ABL)+area(△CMD)+area(Trap.PNEF)+area(Trap.LMCB)=24+30+32+9+100+70=265cm 2