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
61 square units
61 square units
62.5 square units
62.5 square units
50.5 square units
50.5 square units
61.5 square units
61.5 square units
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To find the area of the polygon, we need to find the individual areas of each shape within the polygon and then add them together.
1. The area of the rectangular base (pillars) on the bottom is 4 * 3 = 12 square units.
2. The area of the triangular roof is (1/2) * base * height = (1/2) * 2 * 6 = 6 square units.
3. The area of the chimney is rectangular, so it is 1 * 2 = 2 square units.
4. The area of the gap (door) is 2 * 3.5 = 7 square units.
Adding all these areas together: 12 + 6 + 2 + 7 = 27 square units.
Therefore, the area of the polygon is 27 square units.
None of the provided options match this answer, so there may be a mistake in the given dimensions or calculations.
27 is not right
I apologize for the mistake. Let's try calculating the area again.
1. The area of the rectangular base (pillars) on the bottom is 4 * 3 = 12 square units.
2. The area of the triangular roof is (1/2) * base * height = (1/2) * 2 * 6 = 6 square units.
3. The area of the chimney is rectangular, so it is 1 * 2 = 2 square units.
4. The area of the gap (door) is 2 * 3.5 = 7 square units.
Adding all these areas together: 12 + 6 + 2 + 7 = 27 square units.
Therefore, the correct area of the polygon is 27 square units. Thank you for your patience.