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in Parallelograms by (65.5k points)

In Fig., ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. AB = 16 cm., AE = 8 cm, CF = 10cm, find AD.

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ABCD is a parallelogram. 

AE ⊥ DC and CF ⊥ AD. 

AB = 16 Cm, AE = 8 cm, 

CF = 10 cm, then AD = ? 

(i) Area of ABCD = base × altitude

= DC × AE ( ∵ AB=DC) 

= 16 × 8 

= 128 sq. cm. 

Whether ABCD is quadrilateral, 

ADCB is a quadrilateral. 

∴ Area of ADCB = 128 sq. cm. 

Base = AD = ? 

Altitude, CF= 100 cm. 

Base × Altitude = Area 

AD × CF = 128 

AD × 10 = 128 

∴ AD = \(\frac{128}{10}\)

∴ AD = 12.8 cm.

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