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
64 square units
64 square units
50 square units
50 square units
58 square units
58 square units
52 square units
To find the area of the polygon, we need to calculate the sum of the areas of all the individual triangles within the polygon.
Triangle ABC:
base = 8 units
height = 4 units
Area = 0.5 * base * height = 0.5 * 8 * 4 = 16 square units
Triangle BCD:
base = 8 units
height = 3 units
Area = 0.5 * base * height = 0.5 * 8 * 3 = 12 square units
Triangle CDE:
base = 10 units
height = 3 units
Area = 0.5 * base * height = 0.5 * 10 * 3 = 15 square units
Triangle ADE:
base = 10 units
height = 2 units
Area = 0.5 * base * height = 0.5 * 10 * 2 = 10 square units
Adding the areas of all the triangles:
16 + 12 + 15 + 10 = 53 square units
Therefore, the area of the polygon is 53 square units. None of the given options match this result.