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
61 square units
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page 9
To find the area of the polygon, we first need to break it down into its individual shapes and calculate their areas separately.
1. The base of the house is a rectangle with dimensions 4 x 3, so the area of the base is 4 x 3 = 12 square units.
2. The triangular roof has a base of 2 (the gap between the two pillars) and a height of 6, so the area of the triangular roof is 0.5 x base x height = 0.5 x 2 x 6 = 6 square units.
3. The chimney is also a triangle with base of 1 and height of 2, so the area of the chimney is 0.5 x base x height = 0.5 x 1 x 2 = 1 square unit.
Adding up the areas of these shapes:
12 (base) + 6 (roof) + 1 (chimney) = 19 square units.
However, we need to consider the two vertical pillars on the base of the house. The area between the base and the top of the pillars is 3.5 x 2 = 7 square units.
Adding this area to the total gives:
19 (previous total) + 7 = 26 square units.
Therefore, the area of the entire polygon is 26 square units.
However, it seems that the answer choices provided do not include this option. Please let me know if further assistance is needed.