Find the area of the polygon.Assume that segments that appear congruent are congruent and angles to be right angles are right angles
To find the area of the polygon, we need to break it down into smaller shapes whose areas we can calculate.
Looking at the polygon, we can see that it consists of two rectangles and two right triangles.
First, let's find the area of the rectangles:
Rectangle 1:
Length = 8 units
Width = 3 units
Area = Length x Width
Area = 8 units x 3 units
Area = 24 square units
Rectangle 2:
Length = 6 units
Width = 3 units
Area = Length x Width
Area = 6 units x 3 units
Area = 18 square units
Next, let's find the area of the two right triangles:
Triangle 1:
Base = 2 units
Height = 3 units
Area = (1/2) x Base x Height
Area = (1/2) x 2 units x 3 units
Area = 3 square units
Triangle 2:
Base = 4 units
Height = 3 units
Area = (1/2) x Base x Height
Area = (1/2) x 4 units x 3 units
Area = 6 square units
Now, we add the areas of all the shapes together:
Area = Area of Rectangle 1 + Area of Rectangle 2 + Area of Triangle 1 + Area of Triangle 2
Area = 24 square units + 18 square units + 3 square units + 6 square units
Area = 51 square units
Therefore, the area of the polygon is 51 square units.