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D (-1/2, 5/2), E (7, 3) and F (7/2, 7/2) are the midpoints of sides AB, BC and CA respectively. ABC is a triangle.

Area of triangle DEF :

The triangles ADE, BDF, DEF, EFC are all of equal size. The reason is DE = 1/2 BC and Δ ADE is similar to Δ ABC. Hence, area of Δ ADE = 1/4 * area of Δ ABC.

Area of triangle ABC = 1/2[ x1(y2 - y3) + x2 (y3 - y1) + x3 (y1 - y2) ]
Area of triangle ABC = 4 area of triangle DEF
Area of triangle DEF = 1/2[-1/2(3 - 7/2) + 7(7/2 - 5/2) + 7/2(5/2 - 3)]
Area of triangle DEF = 1/2[ 1/4 +7 -7/4]
Area of triangle DEF = 22/8
Area of triangle ABC = 4 area of triangle DEF
Area of triangle ABC = 4*22/8
Area of triangle ABC = 11