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 square units
61 square units
61.5 square units
61.5 square units
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To find the area of the polygon, we need to break it down into basic shapes and calculate their areas separately.
First, we calculate the area of the rectangular base:
Area = length x width
Area = 4 x 3
Area = 12 square units
Next, we calculate the area of the triangular roof:
Area = 0.5 x base x height
Area = 0.5 x 2 x 6
Area = 6 square units
Now, we calculate the area of the triangle on top of the roof (chimney):
Area = 0.5 x base x height
Area = 0.5 x 1 x 2
Area = 1 square unit
The total area of the polygon is the sum of the areas of the above shapes:
12 + 6 + 1 = 19 square units
Therefore, the correct answer is not provided in the list. The actual area of the polygon is 19 square units.