Area of Polygons Quick Check

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A polygon shows an outline in the shape of a house with a triangular roof, a door and a chimney, standing on two base pillars. The length of the two rectangular pillars is 4 and the width is 3. The gap between the two pillars, or the door, measures 2 across and the inner side of the vertical pillars measures 3.5. The perpendicular height of the triangular roof is 6. The sides of the triangle base extending outward from the outer side of both pillars is 2. The sides of the chimney sitting on the slanted roof on the right measure 1 and 2 and its thickness is 1.

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)
Responses

61 square units
61 square units

50.5 square units
50.5 square units

61.5 square units
61.5 square units

62.5 square units
62.5 square units
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Answer 1

To find the area of the polygon, we first need to find the area of each individual shape.

1. Rectangle (pillar): Area = length x width = 4 x 3 = 12 square units (for each pillar, total of 24 square units)
2. Door (rectangle): Area = length x width = 2 x 3.5 = 7 square units
3. Triangle (roof): Area = 1/2 x base x height = 1/2 x 10 x 6 = 30 square units
4. Triangle (chimney): Area = 1/2 x base x height = 1/2 x 3 x 1 = 1.5 square units
5. Trapezoid (chimney): Area = 1/2 x (base 1 + base 2) x height = 1/2 x (2 + 1) x 1 = 1.5 square units

Total area: 24 + 7 + 30 + 1.5 + 1.5 = 64 square units

Therefore, the correct answer is not listed in the options provided. The correct area of the polygon is 64 square units.