MCQ
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 $a \|gm\ \text{ABCD},$ 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 $a \|gm =\frac{1}{2}\times\text{base}\times\text{altitude}.$ Which is true?

  • A
    $I$ only
     
  • B
    $II$ only
     
  • $I$ and $II$
     
  • D
    $II$ and $III$

Answer

Correct option: C.
$I$ and $II$
 
Since the parallelogram and the rectangle are on the same base and between the same parallels, they are equal in area.
So, the statement $(I)$ is true.

$\text{ar}(\|gm\ \text{ABCD}) = AB \times DE = 10 \times 6\ cm^2$
Similarly,
$\text{ar}(\|gm \ \text{ABCD}) = AD \times BF = AD \times 8$
$\Rightarrow AD \times 8 = 60$
$\Rightarrow AD = 7.5\ cm$
So, $(II)$ is true.
$\text{ar}(\|gm) =$ base $\times$ altitude
So, $(III)$ is false.

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