As shown in the figure, in triangle ABC, G is the midpoint of AC, D, E and F are the four dividing points of BC, and the area of triangle ABD is 72 square centimeters larger than that of quadrilateral CFNG. The parallel line of BG passing through C intersects the extension line of AF at H ..

Easy NG? HC？ =? 1? ﹕2? (midline theorem)

Easy to get △BNF∽△CHF? , get BN? :? CH？ =? BF？ :? CF？ =? 3? :? 1

To sum up, get BN? :? NG？ =? 6? : 1

If the area of △ANG is 6, the area of △ABN is 6? ×6? =36 (equal height, 6 times length of bottom)

The area of △ABC is (36? +? 6)×? 2? =84

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