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AreaAreas of Parallelograms and Triangles — Maths STD 9 — Question

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

Answer

Correct option: B.
$128 \mathrm{~cm}^2$

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

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