2. Questions Bank
  3. 9th Class
  4. Mathematics
  5. Areas of Parallelograms and Triangles

9th Class Mathematics Areas of Parallelograms and Triangles Question Bank Area of Parallelogram & Triangle

  • question_answer
    ABC is an equilateral triangle. P and Q are two points on \[\overline{\mathbf{AB}}\] and \[\overline{\mathbf{AC}}\] respectively such that\[\mathbf{PQ}\parallel \mathbf{BC}\]. If \[\overline{\mathbf{PQ}}=\mathbf{3}\]cm, then area of \[\Delta \mathbf{APQ}\] is:

    A)  \[\frac{25}{4}\]sq.cm               

    B)  \[\frac{25}{\sqrt{3}}\]sq.cm

    C)  \[\frac{9\sqrt{3}}{4}\]sq.cm  

    D)  \[25\sqrt{3}\]sq.cm

    Correct Answer: C

    Solution :

    (c): \[PQ\parallel BC\]  Also, \[\angle APQ=\angle ABC={{60}^{{}^\circ }}\] \[\angle AQP=\angle ACB={{60}^{{}^\circ }}\] \[\therefore \]Area of \[\Delta APQ=\frac{\sqrt{3}}{4}\times {{\left( PQ \right)}^{2}}=\frac{\sqrt{3}}{4}\times {{\left( 3 \right)}^{2}}=\frac{9\sqrt{3}}{4}\]sq.cm         


You need to login to perform this action.
You will be redirected in 3 sec spinner