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 square units
61 square units
50.5 square units
50.5 square units
61.5 square units
61.5 square units
62.5 square units
To find the area of the polygon, we can break it down into smaller shapes and then find the areas of each shape separately.
1. Find the area of the triangular roof:
Area = (1/2) * base * height
Area = (1/2) * 2 * 6
Area = 6 square units
2. Find the area of the rectangular base with a gap for the door:
Area = length * width
Area = (4 + 4) * 3
Area = 24 square units
3. Find the area of the rectangular door:
Area = length * width
Area = 2 * 3.5
Area = 7 square units
4. Find the area of the chimney:
Area = 1 * 2 = 2 square units
Total area = 6 (triangle) + 24 (rectangular base) + 7 (door) + 2 (chimney) = 39 square units
Therefore, the area of the polygon is 39 square units.