Find the area of pentagon ABCDE in which and such that cm, cm, cm, cm, cm and cm.

Given: A pentagon ABCDE


and


cm


cm


cm


cm


cm


cm


MC = AC – AM = 18 – 14 = 4 cm


MN = AM – AN = 14 – 6 = 8 cm


Here,


Area (Pent. ABCDE) = area (AEN) + area (DMC) + area (ABC) + area (Trap. DMNE)


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


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


Here,


Area (AEN) = × (AN) × (EN) = × (6) × (9) = 27 cm2.


Area (DMC) = × (MC) × (DM) = × (4) × (12) = 24 cm2.


Area (ABC) = × (AC) × (BL) = × (18) × (4) = 36 cm2.


Area (Trap. DMNE) = × (DM + EN) × MN = × (12 + 9) × 8 = 84 cm2.


Area (Pent. ABCDE) = area (AEN) + area (DMC) + area (ABC) + area (Trap. DMNE)


= 27 + 24 + 36 + 84 = 171 cm2.


Area (Pent. ABCDE) = 171 cm2.


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