A ballroom in a hotel has the shape shown in the diagram. The hotel manager needs to determine how much carpet is needed to reca
rpet this area. All angles are right angles. The area of the ballroom is
2 answers:
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Answer:
Figure 1's surface area: 550
Figure 2's surface area: 530
Figure 3's surface area: 790
So, the order of the figures' surface areas is: Figure 2 < Figure 1 < Figure 3.
Step-by-step explanation:
Bearing in mind that the surface area of a 3D object is the total area of its surface (that is the sum of the areas of its faces), we can count the number of distinct shapes in each figure, calculate their areas and add them up. Be careful not to add the faces that are "inside".
<u>Figure 1</u>
Its surface area consists of 13 squares of 5x5and 3 rectangles of 15x5
. So, its surface area is (13x25 + 3x75)
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<u>Figure 2</u>
Its surface area consists of 6 squares of 5x5, 3 rectangles of 17x5
, 1 rectangle of 13x5
and 2 triangles of base 12 feet and height 5 feet. So, its surface area is (17x5x3+6x5x5+13x5+12x5x2:2)
<u />
<u>Figure 3</u>
Its surface area consists of 2 rectangles of 12.5x5, 1 rectangle of 11x5
, 2 triangles of base 12 feet and height 5 feet, 1 rectangle of 11x13
, 2 rectangles of 12.5x11
and 1 rectangle of 12x11
.
So, its surface area is (2x12.5x5+11x5+2x12x5:2+11x13+2x12.5x11+12x11)
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