Given: A Hexagon ABCDE

and

cm

cm

cm

cm

cm

cm

cm

cm

cm

AL = AP + PL = 6 + 2 = 8 cm

PN = PL + LN = 2 + 8 = 10 cm

LM = LN + NM = 8 + 2 = 10 cm

ND = NM + MD =2 + 3 = 5 cm

Here,

Area (Hex. ABCDEF) = area (APF) + area (DEN) + area (ABL) + area (CMD)

+ area (Trap. PNEF) + area (Trap. LMCB)

Area of triangle = × (base) × (height).

Area of trapezium is × (sum of parallel sides) × height

Here,

Area (APF) = × (AP) × (FP) = × (6) × (8) = 24 cm².

Area (DEN) = × (ND) × (EN) = × (5) × (12) = 30 cm².

Area (ABL) = × (AL) × (BL) = × (8) × (8) = 32 cm².

Area (CMD) = × (MD) × (CM) = × (3) × (6) = 9 cm².

Area (Trap. PNEF) = × (FP + EN) × PN = × (8 + 12) × 10 = 100 cm².

Area (Trap. LMCB) = × (BL + CM) × LM = × (8 + 6) × 10 = 70 cm².

Area (Hex. ABCDEF) = area (APF) + area (DEN) + area (ABL) + area (CMD)

+ area (Trap. PNEF) + area (Trap. LMCB) = 24 + 30 + 32 + 9 + 100 + 70 = 265 cm².

Area (Hex. ABCDEF) = 265 cm²