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AreaAreas of Parallelograms and Triangles — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSAreaAreas of Parallelograms and Triangles1 Mark
MCQ
Which of the following is a false statement?
  • A
    If the diagonals of a rhombus are $18\ cm$ and $14\ cm,$ then its area is $126\ cm^2.$
  • ✓
    Area of a $\|gm =\frac{1}{2}\times$ base $\times$ corresponding height.
  • C
    A parallelogram and a rectangle on the same base and between the same parallels are equal in area.
  • D
    If the area of a $\|gm$ with one side $24\ cm$ and corresponding height h cm is $192\ cm^2,$ then $h = 8\ cm.$
✓

Answer

Correct option: B.
Area of a $\|gm =\frac{1}{2}\times$ base $\times$ corresponding height.
$a.$ The area of the rhombus $=\frac{1}{2}\times$ product of the diagonals
$=\frac{1}{2}\times18\times14$
$=126 \ cm^2$
So, the statement is true.
$b.$ area of a $\|gm =$ base $\times$ height
So, the statement is false.
$c.$Since parallelograms between the same parallel lines and on the same base are equal in area, and a rectangle is a $\|gm$, the statement is true.
$d.$ area of a $\|gm =$ base $\times$ height
$\Rightarrow 192 = 24 \times h$
$\Rightarrow h = 8\ cm$
So, the statement is true.

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