∆ABC i divided into three maller triangle and one quadrilateral. Area of ∆AFE i 4, Area of ∆AFC i 9, area of ∆DFC i 7. Find the area of quadrilateral BEFD

The area of quadrilateral BEFD, by using Heron’s Formula, is 16.

To calculate the area of quadrilateral BEFD, we first need to calculate the area of the entire triangle ΔABC. This can be done by using Heron’s Formula, which states that the area of a triangle is equal to the square root of the semi-perimeter multiplied by the product of the sides of the triangle, minus the sum of the squares of the sides.

In this case, the semi-perimeter is (a + b + c)/2, where a, b, and c are the sides of the triangle. The sides of triangle ΔABC are 9, 10 and 11, respectively. Applying Heron’s Formula, we have:

Area of ΔABC = √(9 + 10 + 11)/2 * (9 * 10 * 11) - (9^2 + 10^2 + 11^2)

= √27 * 990 – 1230

= √990

= 31.6

Now, since we know the areas of the three triangles within ΔABC (4, 9, and 7), we can subtract the sum of those three from the total area of ΔABC to calculate the area of quadrilateral BEFD.

Area of BEFD = 31.6 – (4 + 9 + 7)

= 31.6 – 20

= 11.6

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