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
50.5 square units
61.5 square units
62.5 sqaure units
To find the area of the polygon, we need to break it down into basic shapes and calculate their individual areas.
1. The rectangular base of the house (including the gap for the door) has dimensions 4 by 3, giving it an area of 4 * 3 = 12 square units.
2. The triangular roof has a base of 4 units and a height of 6 units. The area of a triangle is calculated as 0.5 * base * height, so the area is 0.5 * 4 * 6 = 12 square units.
3. The two rectangles on the sides of the house have dimensions 3.5 by 2. The area of each rectangle is 3.5 * 2 = 7 square units, so for both sides, it's 2 * 7 = 14 square units.
4. The chimney is a smaller rectangular prism with dimensions 1 by 2 by 1. The area of all its faces is 2 * (1 * 2 + 1 * 1 + 2 * 1) = 10 square units.
Adding up all these areas, we get 12 (base of house) + 12 (roof) + 14 (sides) + 10 (chimney) = 48 square units.
Therefore, the area of the polygon is 48 square units.
Since 48 is not one of the provided options, we need to re-evaluate our calculations. Let's look at the roof area calculation:
The triangular roof has a base of 4 units and a height of 6 units. The area of a triangle is calculated as 0.5 * base * height, so the area is 0.5 * 4 * 6 = 12 square units.
Adding 12 (base of house) + 12 (roof) + 14 (sides) + 10 (chimney) = 48 square units.
Therefore, the area of the polygon is 48 square units.
None of the provided options match exactly, but the closest is 50.5 square units.