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rjkz [21]
3 years ago
6

Find the TSA for the trapezoidal prism

Mathematics
1 answer:
8090 [49]3 years ago
4 0

Answer:

TAS = 43.99 m²

Step-by-step explanation:

  • TSA = total surface area
  • Area of a trapezoid = (1/2)(a + b)h
    (where a and b are the parallel sides and h is the height)
  • Area of a rectangle = width x length

This prism is made up of 4 rectangles and 2 congruent trapezoids.

Area of trapezoid = (1/2) x (1.4 + 2.3) x 1.9 = 3.515 m²

⇒ area of 2 trapezoids = 3.515 x 2 = 7.03 m²

Area of base rectangle = 2.3 x 4.8 = 11.04 m²

Area of top rectangle = 1.4 x 4.8 = 6.72 m²

Area of back rectangle = 1.9 x 4.8 = 9.12 m²

Area of sloped rectangle = 2.1 x 4.8 = 10.08 m²

Total surface area = 7.03 + 11.04 + 6.72 + 9.12 + 10.08 = 43.99 m²

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Answers:

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==========================================================

Work Shown:

q = number of quarters

n = number of nickels

q+n = 46 coins total which solves to n = 46-q

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5n = value of all the nickels in cents

25q+5n = value (cents) of all the coins of both types

25q+5n = 710 cents total = $7.10

-------------

Apply substitution.

25q+5n = 710

25q+5(46-q) = 710

25q+230-5q = 710

20q+230 = 710

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This yields 25*q = 25*24 = 600 cents = $6.00 so far.

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They also have 22 nickels.

They have an additional 5n = 5*22 = 110 cents = $1.10

In total, they have 6.00+1.10 = 7.10 dollars which confirms we have the correct coin counts. Also, q+n = 24+22 = 46.

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