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
62.5 square units
62.5 square units
61 square units
61 square units
50.5 square units
61.5 square units
To find the area of the polygon, we need to break it down into smaller shapes and find their areas separately.
1. The triangular roof:
The base of the triangular roof is formed by the sides of the triangle extending outward from the outer side of both pillars, which have a length of 2. The height of the triangular roof is given as 6. Therefore, the area of the triangular roof is (1/2) * base * height = (1/2) * 2 * 6 = 6 square units.
2. The rectangular base:
The length of the rectangular base is given as 4 and the width is given as 3. Therefore, the area of each rectangular base is length * width = 4 * 3 = 12 square units. Since there are two rectangular bases, the total area of the rectangular base is 2 * 12 = 24 square units.
3. The door:
The width of the door is given as 2 and the height is given as the inner side of the vertical pillars, which is 3.5. Therefore, the area of the door is length * width = 2 * 3.5 = 7 square units.
4. The chimney:
The chimney can be seen as a trapezoid. The length of the top base of the trapezoid is given as 1, the length of the bottom base is given as 2, and the height is given as the thickness of the chimney, which is 1. Therefore, the area of the trapezoid chimney is (1/2) * (top base + bottom base) * height = (1/2) * (1 + 2) * 1 = 1.5 square units.
Now, to find the total area of the polygon, we add the areas of these individual shapes together:
Total area = Area of triangular roof + Area of rectangular base + Area of door + Area of chimney
= 6 + 24 + 7 + 1.5
= 38.5 square units.
Therefore, the correct answer is 38.5 square units.