Answer:
772.4 ft^2
Step-by-step explanation:
find the area of each face. first the slanted rectangle. the dimensions of the slanted rectangle are 21.7ft by 12ft. so the area is 21.7*12=260.4ft^2. for the two triangles on the sides, each on has an area of 20*8.5/2=85. next for the smaller rectangle, the dimensions are 12ft by 8.5ft giving us an area of 102 ft^2. lastly for the base, it has dimensions of 20ft by 12ft giving us an area of 240ft^2. now you just add up all the areas: 260.4+85+85+102+240=772.4 (you might want to check my addition just in case)
From calculations, we can say that the given tiles will not fit together perfectly.
<h3>How to find the sum of interior angles of a Polygon?</h3>
If the tiles join perfectly at a point, sum of all angles around the joining point should be 360°.
Expression for the measure of the interior angle of a polygon,
Interior angle of a polygon = [(n - 2) * 180]/n
Interior angle of a pentagon = [(5 - 2) * 180]/5 = 108°
Interior angle of a hexagon = [(6 - 2) * 180]/6 = 120°
Interior angle of an octagon = [(8 - 2) * 180]/8 = 135°
To prove that the given tiles fit together perfectly → Sum of all the angles around the common point should be 360°
Sum of all interior angles = 108° + 120° + 135° = 363°
Therefore, given tiles will not fit together perfectly.
Read more about Interior angles of a Polygon at; brainly.com/question/224658
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