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
62.5 square units
62.5 square units
50.5 square units
50.5 square units
61.5 square units
61.5 square units
61 square units
61 square units
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To calculate the area of the polygon, break it down into smaller shapes.
1. Calculate the area of the rectangular base: 4 * 3 = 12 square units for each rectangle, so total area = 2 * 12 = 24 square units.
2. Calculate the area of the gap between the rectangles (door): 2 * 3.5 = 7 square units.
3. Calculate the area of the triangular roof: (1/2) * base * height = (1/2) * 2 * 6 = 6 square units.
4. Calculate the area of the chimney: (1/2) * base1 * base2 * height = (1/2) * 1 * 2 * 1 = 1 square unit.
Add these areas together:
24 square units (rectangular base) + 7 square units (door gap) + 6 square units (triangular roof) + 1 square unit (chimney) = 38 square units.
Therefore, the correct answer is not listed, but the actual area of the polygon is 38 square units.
what is the answer
I apologize for the oversight in my previous responses. Let's recalculate the area of the polygon:
1. Calculate the area of the rectangular base: 4 * 3 = 12 square units for each rectangle, so total area = 2 * 12 = 24 square units.
2. Calculate the area of the gap between the rectangles (door): 2 * 3.5 = 7 square units.
3. Calculate the area of the triangular roof: (1/2) * base * height = (1/2) * 2 * 6 = 6 square units.
4. Calculate the area of the chimney: (1/2) * base1 * base2 * height = (1/2) * 1 * 2 * 1 = 1 square unit.
Add these areas together:
24 square units (rectangular base) + 7 square units (door gap) + 6 square units (triangular roof) + 1 square unit (chimney) = 38 square units.
Therefore, the correct answer is 38 square units.