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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
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
From the answer choosies
61.5 square units
To find the area of the polygon, we need to break it down into smaller shapes and add up their areas.
1. The base of the house is a rectangle with sides of length 4 and width 3, so the area is 4 * 3 = 12 square units.
2. The triangular roof can be divided into two smaller right triangles. The area of each triangle is (1/2) * base * height. So, the area of each triangle is (1/2) * 2 * 6 = 6 square units. Since there are two triangles, the total area of the roof is 6 + 6 = 12 square units.
3. The chimney can be divided into a rectangle and a triangle. The area of the rectangle is 1 * 2 = 2 square units. The area of the triangle is (1/2) * 1 * 1 = 0.5 square units. So, the total area of the chimney is 2 + 0.5 = 2.5 square units.
4. The inner space of the house is a rectangle with sides of length 2 and width 3.5, so the area is 2 * 3.5 = 7 square units.
5. The gap between the two pillars is also a rectangle with sides of length 2 and width 3, so the area is 2 * 3 = 6 square units.
Adding up all the areas:
12 (base) + 12 (roof) + 2.5 (chimney) + 7 (inner space) + 6 (gap) = 39.5 square units.
Since the house is open on one side, the total area should be doubled:
39.5 * 2 = 79 square units.
Therefore, the area of the polygon is 79 square units.