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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. Help pls
To find the area of the polygon, we will break it down into smaller shapes and calculate the area of each.
1. Start by calculating the area of the rectangular base:
Area = length x width
Area = 4 x 3
Area = 12 square units
2. Next, calculate the area of the triangular roof:
The base of the triangle (the width of the house) is 4 units.
The height of the triangle is given as 6 units.
Area = 0.5 x base x height
Area = 0.5 x 4 x 6
Area = 12 square units
3. Calculate the area of the door (the gap between the pillars):
Area = width x height
Area = 2 x 3.5
Area = 7 square units
4. Calculate the area of the chimney:
The chimney is made up of a rectangle and a triangle.
Rectangle area = width x height = 1 x 1 = 1 square unit
Triangle area = 0.5 x base x height = 2 x 1 = 1 square unit
Total chimney area = 1 + 1 = 2 square units
5. Calculate the total area of the polygon:
Total area = rectangular base area + triangular roof area + door area + chimney area
Total area = 12 + 12 + 7 + 2 = 33 square units
Therefore, the area of the polygon is 33 square units.
Wrong
Apologies for the error. Let's try again:
To find the area of the polygon, we need to break it down into smaller shapes and calculate their areas.
1. Calculate the area of the rectangular base:
Area = length x width
Area = 4 x 3
Area = 12 square units
2. Calculate the area of the triangular roof:
The base of the triangle (the width of the house) is 4 units.
The height of the triangle is given as 6 units.
Area = 0.5 x base x height
Area = 0.5 x 4 x 6
Area = 12 square units
3. Calculate the area of the door (the gap between the pillars):
The door is a rectangle with dimensions 2 (width) x 3.5 (height).
Area = width x height
Area = 2 x 3.5
Area = 7 square units
4. Calculate the area of the chimney:
The chimney consists of a rectangle and a triangle.
Rectangle area = width x height = 1 x 1 = 1 square unit
Triangle area = 0.5 x base x height = 1 x 2 x 1 = 1 square unit
Total chimney area = 1 + 1 = 2 square units
5. Calculate the total area of the polygon:
Total area = rectangular base area + triangular roof area + door area + chimney area
Total area = 12 + 12 + 7 + 2 = 33 square units
Therefore, the area of the polygon is 33 square units.
Bro that’s not right
Apologies for the mistake again. Let's break down the polygon into smaller shapes and calculate the area correctly.
To find the total area of the polygon, we can break it down into five shapes: two rectangles, two triangles, and a parallelogram.
1. Calculate the area of the rectangular base:
Area = length x width
Area = 4 x 3
Area = 12 square units
2. Calculate the area of the triangular roof:
The base of the triangle is the width of the house, so base = 4 units.
The height of the triangle is 6 units.
Area = 0.5 x base x height
Area = 0.5 x 4 x 6
Area = 12 square units
3. Calculate the area of the smaller triangle for the roof over the door:
Base = 2 units and height = 3.5 units
Area = 0.5 x base x height
Area = 0.5 x 2 x 3.5
Area = 3.5 square units
4. Calculate the area of the parallelogram shape formed by the roof and chimney:
The base of the parallelogram is 2 units (distance between pillars)
The height of the parallelogram is 2 units (height of the chimney)
Area = base x height = 2 x 2 = 4 square units
5. Calculate the area of the chimney:
The chimney consists of a rectangle and a triangle.
Rectangle area = width (1) x height (2) = 1 x 2 = 2 square units
Triangle area = 0.5 x base (1) x height (1) = 0.5 x 1 x 1 = 0.5 square units
Total chimney area = Rectangle area + Triangle area = 2 + 0.5 = 2.5 square units
Total area = Rectangle base area + Triangular roof area + Triangular roof over door area + Parallelogram area + Chimney area
Total area = 12 + 12 + 3.5 + 4 + 2.5
Total area = 34 square units
Therefore, the correct total area of the polygon is 34 square units. Thank you for your patience.