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Answer 1

Step-by-step explanation:

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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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Solution

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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=80cm

2

--- ( 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=

12

80

∴ AD=6.66cm

Answer 2

Step-by-step explanation:

Area of parallelogram = base × height

if we take AB as base then AE is height

in this case area will be given by= AB×AE

if we take AD as base then CF is height

in this case area = AD×CF

area calculated from taking different side as base of same parallelogram

now both area should be same as it area of same parallelogram

so AB×AE=AD×AE

AD=AB×AE/CF

=17×8/10

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