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
61.5 square units
61.5 square units
50.5 square units
50.5 square units
61 square units
61 square units
62.5 square units
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.
1.61.5 square units
2.50.5 square units
3.61 square units
4.62.5 square units
To find the area of the polygon, we need to calculate the area of each individual shape and then add them up.
1. Start with the rectangular base: 4 x 3 = 12 square units (x2 since there are 2)
2. Add the triangle on top of the rectangular base: (1/2) x base x height = (1/2) x 2 x 6 = 6 square units
3. Add the chimney: (1 x 2) + (1 x 2) = 4 square units
Total area = 12 (rectangular base) + 12 (triangle) + 4 (chimney) = 28 square units
The area of the polygon is 28 square units.
Therefore, none of the provided options are correct. The correct answer should be 28 square units.
To find the area of each individual shape and then add them up:
1. Rectangular base: Area = 4 x 3 = 12 square units (x2 because there are 2 pillars)
2. Triangle roof: Area = (1/2) x base x height = (1/2) x 2 x 6 = 6 square units
3. Door (gap between pillars): Area = 2 x 3.5 = 7 square units
4. Chimney: Area = (1 x 1) + (1 x 2) = 3 square units
Total area = 12 (rectangular base) + 6 (triangle roof) + 7 (door) + 3 (chimney) = 28 square units
Therefore, the total area of the polygon is 28 square units, which is not provided in the options.