Question

ABCD is a parallelogram. CE is the height from C to AB and a CF also the height from C to AD.If AB=12.9 cm and CE=8.7 cm.Find: (i) the area of the parallelogram ABCD (ii)CF,if AD=6.3​

Answer 1

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Question



In given figure, ABCD is a parallelogram. AE is perpendicular on DC and CF is perpendicular on AD.

If AB = 10 cm, AE = 8 cm and CF = 12 cm. Find AD.





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 In  parallelogram ABCD, we have given AB=10cm, AE=8cm, and CF=12cm.

⇒  AB=DC=10cm         [Opposite sides of parallelogram are equal]

⇒  Lets find out area of parallelogram with height AE and base DC.

⇒  Area of parallelogram ABCD=b×h

⇒  Area of parallelogram ABCD=DC×AE

⇒  10×8

∴   Area of parallelogram ABCD=80cm2   --- ( 1 )

⇒  Now, to find area of parallelogram let CF be the height and AD will be base.

⇒  Area of parallelogram ABCD=CF×AD

⇒  80=12×AD       [From ( 1 )]

⇒  AD=1280

∴   AD=6.66cm

Answer 2

(i) The area of parallelogram ABCD is 120 cm²

(ii) CF = 10 cm

Step-by-step explanation:  

ABCD is a parallelogram.  

Please see attachment for figure.

CE is the height from C to AB.  

CE is perpendicular to AB.

where, CE = 8 cm and AB = 15 cm

Area of parallelogram = Product of side to their corresponding height  

Area of parallelogram = AB × CE  

                                    = 15 × 8  

                                   = 120 cm²

Hence, the area of parallelogram ABCD is 120 cm²  

CF is the height from C to AD.

CF is perpendicular to AD.  

Let length of CF is x cm  

where, CF = x cm and AD = 12 cm

Area of parallelogram = AD × CF  

                             120 = 12 × x  

                                x = 10 cm

Hence, the length of CD is 10 cm

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