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The vertices of a Delta ABC are A(4,6), ...

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

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To solve the problem step by step, we will first find the area of triangle ABC and then use the given ratios to find the area of triangle ADE. ### Step 1: Calculate the area of triangle ABC The formula for the area of a triangle given its vertices \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) is: \[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| ...
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