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)
To find the area of the polygon, we will break it down into smaller shapes and calculate their individual areas.
1. Area of rectangular pillars: 4 x 3 = 12 square units (each pillar)
Total area of pillars = 12 x 2 = 24 square units
2. Area of door opening: 2 x 3.5 = 7 square units
3. Area of triangular roof: 1/2 x base x height = 1/2 x 2 x 6 = 6 square units
4. Area of chimney: (1/2 x base1 x height) + (1/2 x base2 x height) + (1 x thickness) = (1/2 x 1 x 2) + (1/2 x 2 x 2) + (1 x 1) = 1 + 2 + 1 = 4 square units
Total area = 24 + 7 + 6 + 4 = 41 square units
Therefore, the area of the polygon is 41 square units.