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52 cm (a) noneABCD is a trapezium in which AB || CD, as shown. The area of thetrapezium is(a) 1350 cm? (b) 1612 cm (c) 1620 cm28 cm28 CM(d) noneE78 cm |
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Answer» -STEP explanation:What would you like to ASK?8thMathsMensurationArea of TrapeziumABCD is a trapezium in whic...MATHSABCD is a trapezium in which AB∥CD; BC and AD are non-parallel SIDES. It is given that AB=75cm,BC=42cm,CD=30cm and AD=39cm. Find the area of the trapezium.MEDIUMShareStudy laterANSWERDraw CE∥DA and CF⊥AB.Therefore, ADCE is a PARALLELOGRAM having AE∥CD and CE∥DA.⇒AD=CE=39cm,DC=AE=30cm and BE=75−30=45cmIn △BCE, by heron's formula we havea=39cm,b=45cm and c=42cm⇒s= 2a+b+c = 239+42+45 =63cm∴ Area of ΔBEC= s(s−a)(s−b)(s−c) = 63(63−39)(63−42)(63−45) cm 2 = 63×24×21×18 cm 2 =756cm 2 Also, Area of ΔBEC= 21 ×base×height⇒ 21 ×45×h=756cm 2 ⇒h=33.6cmSo, Area of trapezium:- = 21 ×(AB+CD)×height= 21 ×(75+30)×33.6=1764cm 2 solution |
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