Find the area of the Pentagon ABCDE in which BL perpendicular to AC , DM perpendicular to AC and EN perpendicular to AC such that AC = 18 cm , AM = 6 cm , DM = 12 cm and EN = 9 cm?
Answers
Answer:
the area of pentagon is 171
Step-by-step explanation:
BL ⊥ AC, DM ⊥ AC and EN ⊥ AC AC=18cm, AM=14cm, AN=6cm, BL=4cm, DM=12cm, EN=9cm MC=AC-AM =18-14 = 4cm MN= AM- AN= 14-6 =8cm By using the formula, Area (pent.ABCDE) = area (△AEN) + area (△DMC) + area (△ABC) + area (Trap.DMNE) Area of triangle= ½ × base × height Area of trapezium = ½ × (sum of parallel sides) × height ∴ lets calculate, Area (△AEN) = ½ (AN) × (EN) = ½ × 6 × 9 = 27cm2 Area (△DMC) =½ (MC) × (DM) = ½ × 4 × 12 = 24cm2 Area (△ABC) =½ (AC) × (BL) = ½ × 18 × 4 = 36cm2 Area (Trap.DMNE) =½ × (DM + EN) × MN = ½ × (12+9) × 8 = 84cm2 ∴ Area (pent.ABCDE) = area (△AEN) + area (△DMC) + area (△ABC) + area (Trap.DMNE) = 27 + 24 + 36 + 84 = 171
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