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6
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Find 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)
To find the area of the polygon, we can divide it into triangles and calculate the area of each triangle.
Lets denote the vertices of the polygon as A, B, C, D, and E.
First, we divide the polygon into triangle ADE, triangle ABD, and triangle ABC.
Calculating the area of triangle ADE:
- AD = 6
- DE = 2
- Angle ADE is a right angle
Area of triangle ADE = (1/2) * AD * DE = (1/2) * 6 * 2 = 6 square units
Calculating the area of triangle ABD:
- AB = 2
- BD = 2
- Angle ABD is a right angle
Area of triangle ABD = (1/2) * AB * BD = (1/2) * 2 * 2 = 2 square units
Calculating the area of triangle ABC:
- AB = 2
- BC = 4
- Angle ABC = 90 degrees
Area of triangle ABC = (1/2) * AB * BC = (1/2) * 2 * 4 = 4 square units
Therefore, the total area of the polygon is the sum of the areas of the triangles:
6 + 2 + 4 = 12 square units
So, the area of the polygon is 12 square units.