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
61.5 square units
61.5 square units
50.5 square units
50.5 square units
61 square units
To find the area of the polygon, we need to break it down into smaller shapes and find the area of each shape individually.
1. The rectangular base:
Area = length * width = 4 * 3 = 12 square units
2. The triangular roof:
Area = 0.5 * base * height = 0.5 * 2 * 6 = 6 square units
3. The gap between the two pillars:
Area = 3.5 * 2 = 7 square units
4. The chimney:
Area = 0.5 * base * height = 0.5 * 1 * 2 = 1 square unit
Now, add the areas of all the shapes together:
12 + 6 + 7 + 1 = 26 square units
Therefore, the area of the polygon is 26 square units.