∆XYZ and ∆PQR are similar and XY : PQ = 6 : 1. Area of ∆PQR is 6 cm². What is the area of ∆XYZ?

∆XYZ and ∆PQR are similar, and XY :  PQ = 6 : 1.

Concept Used:
The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
​$$\frac{\text{Area of } \Delta XYZ}{\text{Area of } \Delta PQR} = \left(\frac{XY}{PQ}\right)^2$$​​

Solution:
​$$\frac{\text{Area of } \Delta XYZ}{6} = \left(\frac{6}{1}\right)^2 \\\frac{\text{Area of } \Delta XYZ}{6} = 36 \\\text{Area of } \Delta XYZ = 36 \times 6 = 216 \, \text{cm}^2$$​​​​