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.
To find the area of the polygon, we need to break it down into smaller shapes and then calculate their individual areas.
1. The area of the rectangular base of the house:
Length = 4, Width = 3
Area = Length x Width = 4 x 3 = 12 units
2. The area of the triangular roof:
Base = 2 units (each side of the triangle extending outward from the outer side of both pillars)
Height = 6 units
Area = 0.5 x Base x Height = 0.5 x 2 x 6 = 6 units
3. The area of the rectangle representing the door:
Length = 2, Width = 3.5 (the inner side of the vertical pillars)
Area = Length x Width = 2 x 3.5 = 7 units
4. The area of the chimney:
Base = 1 unit, Height = 2 units, Thickness = 1 unit
Area = Base x Height = 1 x 2 = 2 units
But since the chimney is a 3D shape, we consider its thickness as well.
Area = 2 x Thickness = 2 x 1 = 2 units
Adding up the areas of all the shapes, we get:
12 (rectangular base) + 6 (triangular roof) + 7 (door) + 2 (chimney) = 27 units
Therefore, the area of the polygon is 27 square units.