Question

3. Find the area of pentagon ABCDE in which BL 1 AC, DM I AC
and EN 1 AC such that AC = 18 cm , AM = 14 cm , AN = 6 cm,
BL = 4 cm, DM = 12 cm and EN = 9 cm.​

Answer 1

Step-by-step explanation:

Find the area of pentagon ABCDE in which BL ⊥ AC, DM ⊥ AC and EN ⊥ AC such that AC = 18 cm, AM = 14 cm, AN = 6 cm, BL = 4 cm, DM = 12 cm and EN = 9 cm. Hence , the area of the given pentagon is 171 cm 2

Answer 2

Answer:

The given details are

, 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