Find the total area of the shaded polygon what is the area of the polygon in square units
To find the total area of the shaded polygon, we need to break it down into smaller shapes that are easier to calculate. In this case, the polygon can be divided into two rectangles and two right triangles.
The area of a rectangle is calculated by multiplying its length by its width. Let's denote the lengths and widths of the rectangles as follows:
Rectangle 1 (top): Length = 9 units, Width = 5 units
Rectangle 2 (bottom): Length = 9 units, Width = 3 units
The area of Rectangle 1 = 9 units x 5 units = 45 square units
The area of Rectangle 2 = 9 units x 3 units = 27 square units
Next, let's calculate the area of the two right triangles. The formula for the area of a triangle is 0.5 x base x height. Let's denote the base and height of the triangles as follows:
Triangle 1 (left): Base = 3 units, Height = 6 units
Triangle 2 (right): Base = 6 units, Height = 4 units
The area of Triangle 1 = 0.5 x 3 units x 6 units = 9 square units
The area of Triangle 2 = 0.5 x 6 units x 4 units = 12 square units
Now, add up the areas of all the shapes within the shaded polygon:
Total area = Area of Rectangle 1 + Area of Rectangle 2 + Area of Triangle 1 + Area of Triangle 2
Total area = 45 square units + 27 square units + 9 square units + 12 square units
Total area = 93 square units
Therefore, the area of the shaded polygon is 93 square units.