Area of Polygons Quick Check

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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

61 square units
61 square units

62.5 square units
62.5 square units

50.5 square units
50.5 square units

Answer 1

To find the area of the polygon, we need to find the individual areas of each shape (rectangles, triangle, and chimney) and then add them up.

Area of rectangular pillars: 4 x 3 = 12 square units for each pillar
Total area of both pillars = 12 + 12 = 24 square units

Area of gap between pillars (door): 2 x 3.5 = 7 square units

Area of triangular roof: (1/2) x base x height = (1/2) x 2 x 6 = 6 square units

Area of chimney: (1/2) x base1 x height + (1/2) x base2 x height = (1/2) x 1 x 1 + (1/2) x 2 x 1 = 1.5 + 1 = 2.5 square units

Total area of the polygon: 24 + 7 + 6 + 2.5 = 39.5 square units

Therefore, the correct answer is not provided in the given options.