Practicing Success
ABC is an equilateral triangle. P, Q and R are the midpoints of sides AB, BC and CA, respectively. If the length of the side of the triangle ABC is 8 cm, then the area of ΔPQR is: |
$\frac{\sqrt{3}}{3} \mathrm{~cm}^2$ $\frac{\sqrt{3}}{4} \mathrm{~cm}^2$ $4 \sqrt{3} \mathrm{~cm}^2$ $8 \sqrt{3} \mathrm{~cm}^2$ |
$4 \sqrt{3} \mathrm{~cm}^2$ |
Side of a triangle a = 8 cm Area of triangle = \(\frac{\sqrt {3 }}{4}\) x \( {a }^{2 } \) = Area of triangle ABC = \(\frac{\sqrt {3 }}{4}\) x 8 x 8 = 16\(\sqrt {3 }\) As we know, if P, Q and R are the mid points of sides AB, BC and CA then, Area of triangle PQR = \(\frac{1}{4}\) x Area of ABC = Area of triangle PQR = \(\frac{1}{4}\) x 16\(\sqrt {3 }\) = 4\(\sqrt {3 }\) \( {cm }^{2 } \). |