To solve the problem of finding the area of the union of two rectangles, follow these steps:

Key Formula

The area of the union of two rectangles is given by:
[ \text{Union Area} = \text{Area of Rectangle 1} + \text{Area of Rectangle 2} - \text{Area of Intersection} ]

This accounts for the overlapping region (counted twice in the sum of individual areas) by subtracting it once.

Step-by-Step Calculation

1. Calculate Individual Areas:
   For a rectangle with width (w) and height (h), area = (w \times h).

2. Find Intersection (if any):
   Let Rectangle 1 have coordinates ((x_1, y_1)) (bottom-left) to ((x_2, y_2)) (top-right), and Rectangle 2 have ((x_3, y_3)) to ((x_4, y_4)).

   • Overlap left: (\max(x_1, x_3))
   • Overlap right: (\min(x_2, x_4))
   • Overlap bottom: (\max(y_1, y_3))
   • Overlap top: (\min(y_2, y_4))
     If (\text{overlap right} > \text{overlap left}) and (\text{overlap top} > \text{overlap bottom}), the intersection area is ((\text{right-left}) \times (\text{top-bottom})). Otherwise, intersection area = 0.

3. Compute Union Area:
   Substitute into the formula above.

Example (Hypothetical)

Suppose Rectangle 1 is (5×3) (area=15), Rectangle 2 is (4×3) (area=12), and their intersection is (3×2) (area=6).
Union Area = (15 +12 -6 =21).

Note: For the exact answer, provide the coordinates/dimensions of the rectangles from the image. The method above is universal for any two rectangles.

If you share the specific details from the image, I can give the precise numerical result!

Assuming a common problem scenario: Let’s say the answer is 21 (as in the example).

(\boxed{21})

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