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.
What is the area of the polygon?
A) 62.5 square units
B) 61.5 square units
C) 61 square units
D) 50.5 square units
There are five parts to the shape: the left pillar, the door gap, the right pillar, the roof, and the chimney.
Left and Right Pillar area:
The area of a rectangle is length x width, so the area of each pillar is 4 x 3 = <<4*3=12>>12 square units.
Because the shape has two pillars, the total area of the shape contributed by the pillars is 12 x 2 = <<12*2=24>>24 square units.
Door Gap area:
The door gap is a rectangle with a length of 2 and a width of 3.5.
The area of the door gap is 2 x 3.5 = <<2*3.5=7>>7 square units.
Triangular Roof area:
Since we need to find the area of a triangle, we'll use the formula: (1/2) x base x height.
The triangles on the sides of the roof have a height of 6 and a base of 2.
Area = (1/2) x 2 x 6 = 6 square units.
We need to multiply this by 2 since there are two triangles: 6 x 2 = <<6*2=12>>12 square units.
The base of the big triangle in the middle is 3 (pillar width) + 2 (door width) + 3 (pillar width) = 8. The height of the triangle is 6.
Area = (1/2) x 8 x 6 = 24 square units.
So the total area of the roof is 12 + 24 = <<12+24=36>>36 square units.
Chimney area:
The chimney is a right triangle with a base of 1 and a height of 2.
The area of the chimney is (1/2) x 1 x 2 = <<(1/2)*1*2=1>>1 square unit.
Total area:
Finally, to find the area of the polygon, we need to add up the areas of the pillars, door gap, roof, and chimney: 24 + 7 + 36 - 1 = 66 square units.
So the area of the polygon is 66 square units, which is not found in any of the options.
The given options must be wrong or additional information is needed to answer this question correctly.