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
To find the area of the polygon, we can break it down into smaller shapes and then add up the areas.
1. The base rectangle has dimensions 4 by 3, so the area is 4 * 3 = 12 square units.
2. The top rectangle has dimensions 4 by 3, so the area is 4 * 3 = 12 square units.
3. The triangle has a base of 6 and a height of 6, so the area is (1/2) * 6 * 6 = 18 square units.
4. The door rectangle has dimensions 2 by 3.5, so the area is 2 * 3.5 = 7 square units.
5. The small triangle on the top right has a base of 1 and a height of 6, so the area is (1/2) * 1 * 6 = 3 square units.
6. The chimney rectangle has dimensions 1 by 2, so the area is 1 * 2 = 2 square units.
Adding up all the areas: 12 + 12 + 18 + 7 + 3 + 2 = 54 square units.
Therefore, the correct answer is not provided in the options given. The correct area of the polygon is 54 square units.