The vertices of a \( \triangle \mathrm{ABC} \) are \( \mathrm{A}(4,6), \mathrm{B}(1,5) \) and \(...

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The vertices of a \( \triangle \mathrm{ABC} \) are \( \mathrm{A}(4,6), \mathrm{B}(1,5) \) and \( \mathrm{C}(7,2) \). A line is drawn to intersect sides \( \mathrm{AB} \) and \( \mathrm{AC} \) at \( \mathrm{D} \) and \( \mathrm{E} \) respectively, such that \( \frac{\mathrm{AD}}{\mathrm{AB}}=\frac{\mathrm{AE}}{\mathrm{AC}}=\frac{1}{4} \). Calculate the area of the \( \triangle \mathrm{ADE} \) and compare it with the area of \( \triangle \mathrm{ABC} \).
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