Question

Look at the statemets given below:

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

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

III.Area of a ||gm=$\frac{1}{2}\times base\times altitude$.

Which is true?

(a) I only

(b) II only

(c) I and II

(d) II and III

Answer 1

ANSWER:
(c) I and II
Statement I is true, because if a parallelogram and a rectangle lie on the same base and between the same
parallel lines, then they have the same altitude and therefore equal areas.
Statement II is also true as area of a parallelogram = base × height
⇒ AB × DE = AD × BF
⇒10 × 6 = 8 × AD
⇒ AD = 60 ÷ 8 = 7.5 cm
Hence, statements I and II are true.