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?

Question

Philoid · Accepted Answer

Consider Statement (I) :

Two or more parallelograms on the same base and between the same parallels are equal in area. Rectangle is also a parallelogram.

∴ It is true.

Consider Statement (II) :

Here, let AB be the base of the parallelogram then DE becomes its altitude (height).

Area of the parallelogram is given by: Base × Height

∴ Area of ‖gm ABCD = AB×DE = 10×6 = 60cm²

Now,

Consider AD as base of the parallelogram then BF becomes its altitude (height)

∴ area of ‖gm ABCD = AD × BF = 60cm²

AD × 8 = 60cm²

AD = = 7.5cm

∴length of AD = 7.5cm.

∴ Statement (II) is correct.

Consider Statement (III)

Area of parallelogram is base× height

∴ Statement (III) is false

∴ Statement (I) and (II) are true and statement (III) is false