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Areas of Parallelograms and Triangles — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsAreas of Parallelograms and Triangles1 Mark
MCQ
In a quadrilateral $\text{ABCD}$, it is given that $BD = 16\ cm.$ If $\text{AL}\perp\text{BD}$ and $\text{CM}\perp\text{BD}$ such that $AL = 9\ cm$ and $CM = 7\ cm,$ then $ar($ quadrilateral $\text{ABCD}) = ?$​​​​​​​
  • A
    $256\ cm^2$
  • ✓
    $128\ cm^2$
  • C
    $64\ cm^2$
  • D
    $96\ cm^2$
✓

Answer

Correct option: B.
$128\ cm^2$
Area of quadrilateral $\text{ABCD} =\text{ar}(\triangle\text{ABD})+\text{ar}(\triangle\text{BCD})$
$=\frac{1}{2}\times\text{BD}\times\text{AL}+\frac{1}{2}\text{BD}\times\text{CM}$
$=\frac{1}{2}\times16\times9+\frac{1}{2}\times16\times7$
$=72+56$
$=128\text{cm}^2$

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