Question

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

Answer 1

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.