Answer:
9
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