The scale on a map is 1 cm : 6.5 mi. the actual distance between amelia's school and her house is 45 miles. how far apart are they on the map?

about 6.9 cm

Step-by-step explanation:

Set up a proportion to solve this problem.

1 cm is to 6.5 miles as x cm is to 45 miles

1/6.5 = x/45           now solve for x by cross multiplying

45 = 6.5x

45/6.5 = x    

  6.923076923 cm = x

Step-by-step explanation:

You can use the same formula in each case. The area of a triangle with sides "a" and "b" separated by angle α is ...

  A = (1/2)ab·sin(α)

1. The area of the square is 4 times the area of the right triangle whose legs are radii of the square:

  square area = 4·(1/2)·(13 m)(13 m)sin(90°) = 2·(13 m)² = 338 m²

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2. The area is ...

  A = (1/2)(8 cm)(12 cm)sin(81°) ≈ 47.4 cm²

For this one, you don't need to work out the answer in detail. You know it will be less than, but nearly, 48 cm², which is half the product of the side lengths.