Tag: area of parallelogram

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Multiple choice maths perimeter and area of rectilinear figures parallelogram and rectangle area of parallelogram area of a parallelogram

A parallelogram has sides $30 m, 70 m$ and one of its diagonals is $80 m$ long. Its area will be

  1. $600\displaystyle m^{2}$
  2. $\displaystyle 1200\sqrt{3}m^{2}$
  3. $1200\displaystyle m^{2}$
  4. $\displaystyle 600\sqrt{3} m^{2}$
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B Correct answer
Explanation
The diagonal of parallelogram divides it into two congruent triangles. 
$\therefore $ Area (parallelogram $ABCD) = 2 \times$ Area $ \left (\Delta ABC  \right ) $
In $ \Delta ABC$,
$ s=\cfrac{80m+ 30m+70m}{2}=\cfrac{180m}{2}=90m$
$ \therefore Area=\sqrt{90\left ( 90-80 \right )(90-30)(90-70)}m^{2}$
$ =\sqrt{90\times10\times60\times20m^{2} }$
$= 600\sqrt{3} m^{2}$

$ \therefore $ Area of parallelogram $ABCD =$$ 2\times 600\sqrt{3}m^{2}$ $ =1200\sqrt{3}m^{2}$