Q25 of 83 Page 356

In the given figure, a ‖gm ABCD and a rectangle ABEF are of equal area. Then,

Given: Area (‖gm ABCD) = Area (rectangle ABEF)


Consider ΔAFD


Clearly AD is the hypotenuse


∴ AD > AF


Perimeter of Rectangle ABEF = 2× (AB + AF) –1


Perimeter of Parallelogram ABCD = 2× (AB + AD) –2


On comparing –1 and –2, we can see that


Perimeter of ABCD > perimeter of ABEF (∵AD > AF)

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Look at the statements given below:

(I) A parallelogram and a rectangle on the same base and between the same parallels are equal in area.


(II) In a ‖gm ABCD, it is given that AB = 10cm. The altitudes DE on AB and BF on AD being 6cm and 8cm respectively, then AD = 7.5 cm.


(III) Area of a ‖gm = x base x altitude.


Which is true?