I have no idea how to solve this

9

Step-by-step explanation:

Consider the polygon to consist of 2 rectangles, rectangle X (The bigger rectangular) and Y(the smaller rectangle), as shown in the diagram attached below.

To find DE + EF, let's find each lengths as follows:

DE = BC - FA

DE = 9 - 5 = 4

EF = AB - DC

EF = 8 - DC (we don't know DC)

Let's find out DC by considering the area of the entire polygon to derive an equation that will enable us to find DC.

Area of a rectangle = L*B

Therefore:

Area of the polygon = Area of rectangle X + Area of rectangle Y

Area of Polygon = (AB*FA) + (DE*DC)

52 = (8*5) + (4*DC)

52 = 40 + (4*DC)

Subtract 40 from both sides

52 - 40 = 4*DC

12 = 4*DC

Divide both sides by 4 to make DC the subject.

12/4 = DC

3 = DC

DC = 3

Thus,

DE + EF = (BC - FA) + (AB - DC)

= (9 - 5) + (8 - 3)

= 4 + 5

= 9

step-by-step explanation:

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step-by-step explanation: