Area of Polygons Quick Check
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Question
Use the image to answer the question.
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
50.5 square units
50.5 square units
61.5 square units
61.5 square units
62.5 square units
62.5 square units
61 square units
The area of the polygon can be calculated by finding the areas of each individual shape within the polygon and summing them together.
1. The area of the rectangular pillars: 4 * 3 = 12 units squared * 2 = 24 units squared.
2. The area of the door: 2 * 3.5 = 7 units squared.
3. The area of the triangular roof: (1/2) * base * height = (1/2) * 2 * 6 = 6 units squared.
4. The area of the triangle base extending outward from the pillars: (1/2) * base * height = (1/2) * 2 * 6 = 6 units squared.
5. The area of the chimney: (1/2) * base * height = (1/2) * 1 * 2 = 1 unit squared.
Adding all these areas together: 24 + 7 + 6 + 6 + 1 = 44 units squared.
Therefore, the area of the polygon is 44 square units.
None of the provided responses are correct.