What is the area of quadrilateral ABFG.? A2x-4cmB,BC,CD,D25cmE,AG,G59cmF E.?

To find the area of quadrilateral ABFG, we need to first find the lengths of the sides of the quadrilateral.

Given:
AB = 2x - 4 cm
BC = CD = D = 25 cm
DE = 59 cm
AG = 2x cm
GF = EF = 25 cm

Since BC = CD = D = 25 cm, we can see that BCDE is a square with side length 25 cm.

Since AG = 2x cm and AB = 2x - 4 cm, we can see that AG = AB + BG. Therefore, BG = AG - AB = 2x - (2x - 4) = 4 cm.

Now, we can see that quadrilateral ABFG can be divided into two triangles: triangle ABG and triangle BGF.

Area of triangle ABG = (1/2) * AB * AG = (1/2) * (2x - 4) * 2x = x(2x - 4) = 2x^2 - 4x

Area of triangle BGF = (1/2) * BG * GF = (1/2) * 4 * 25 = 50 cm^2

Therefore, the total area of quadrilateral ABFG = Area of triangle ABG + Area of triangle BGF
= 2x^2 - 4x + 50

So, the area of quadrilateral ABFG is 2x^2 - 4x + 50 square centimeters.

The area of quadrilateral ABFG cannot be determined with the given information. The length of side DE is not provided, which is necessary to calculate the area of the quadrilateral.