Question

solve for the missing value of the trapezoid.

Explanation:

Step1: Use the property of parallelograms

In a parallelogram, opposite sides are equal. Since \(DS\) and \(DG\) are sides of a parallelogram (assuming \(DS\) is parallel to \(DG\) and \(SG\) is parallel to \(D\)’s opposite side), but wait, actually, looking at the figure, if we consider the left - hand side as a parallelogram (opposite sides are equal) and the right - hand side as a trapezoid. However, if we assume that the figure is composed in a way that the non - parallel sides of the trapezoid and the parallelogram are related. But more accurately, if we consider the fact that in a parallelogram (left - hand shape), opposite sides are equal. But if we use the property of the combined figure (assuming the left - hand shape is a parallelogram and the right - hand shape is a trapezoid), and if we use the mid - segment property (but no, wait, another approach). Wait, actually, if we assume that the figure is such that the side \(DG\) (the unknown) and the side \(EF\) are related through the middle segment. But no, the middle segment of a trapezoid \(EF + DG=2\times19\) (where \(19\) is the length of the mid - segment of the trapezoid formed by combining the two shapes in terms of vertical sides).
Let \(x\) be the length of \(DG\). The formula for the mid - segment \(m\) of a trapezoid is \(m=\frac{a + b}{2}\), where \(a\) and \(b\) are the lengths of the parallel sides. Here, \(m = 19\), \(a=13\), and \(b=x\).

$$19=\frac{13 + x}{2}$$

Step2: Solve the equation for \(x\)

Multiply both sides of the equation \(19=\frac{13 + x}{2}\) by \(2\):

$$19\times2=13 + x$$

$$38=13 + x$$

Subtract \(13\) from both sides:

$$x=38 - 13$$

$$x = 25$$

Answer:

\(25\)