What is the area of the polygon? Assume that segments that appear congruent are congruent and angles that appear to be right angles are right angles.
(1 point)
Responses
36 square units
36 square units
54 square units
54 square units
42 square units
42 square units
72 square units
72 square units
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To calculate the area of the polygon, we need to find the area of each smaller shape within the polygon and then add them all together.
The polygon can be divided into two rectangles and two right triangles.
Rectangle 1: 6 units in length and 6 units in width, so its area is 6 * 6 = 36 square units.
Rectangle 2: 6 units in length and 3 units in width, so its area is 6 * 3 = 18 square units.
Right Triangle 1: Base is 3 units and height is 6 units, so its area is (1/2) * base * height = (1/2) * 3 * 6 = 9 square units.
Right Triangle 2: Base is 6 units and height is 6 units, so its area is (1/2) * base * height = (1/2) * 6 * 6= 18 square units.
Adding all the areas together:
36 (Rectangle 1) + 18 (Rectangle 2) + 9 (Right Triangle 1) + 18 (Right Triangle 2) = 81 square units.
Therefore, the correct answer is not listed here, as the calculated area is 81 square units.