Question

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 = 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 $=\frac{1}{2}\times \mathrm{base}\times \mathrm{altitude}.$
Which is true?
(a) I only
(b) II only
(c) I and II
(d) II and III

Answer 1

(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
$\Rightarrow$AB × DE = AD × BF
$\Rightarrow$10 × 6 = 8 × AD
$\Rightarrow$ AD = 60 ÷ 8 = 7.5 cm
Hence, statements I and II are true.