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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
62.5 square units
62.5 square units
61.5 square units
61.5 square units
61 square units
61 square units
50.5 square units
50.5 square units
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To find the area of the polygon, we can break it down into simpler shapes.
1. The base of the house consists of two rectangles, each with a length of 4 and width of 3. We can find the combined area of the two rectangles:
Area = 2 * (4 * 3) = 2 * 12 = 24 square units
2. The triangular roof has a base of 2 and a height of 6. We can find the area of the triangle:
Area = 0.5 * base * height = 0.5 * 2 * 6 = 6 square units
3. The chimney is a rectangle with a length of 2 and width of 1, sitting on top of the slanted roof. We can find the area of the chimney:
Area = 2 * 1 = 2 square units
Adding the areas of the rectangle base, triangular roof, and chimney together:
24 + 6 + 2 = 32 square units
Therefore, the area of the polygon is 32 square units. None of the provided responses match this value.