Question

A student said that the surface area of the figure below was 57.4 square centimeters. Is the student correct? Explain.

Answer 1

Answer:

  no

Step-by-step explanation:

The surface area is the sum of the areas of the faces.

There are 4 faces that are 5 cm wide. Their respective heights (from front, over the top) are ...

  1 cm, 2.5 cm, 2 cm, 2.3 cm

for a total height of 7.8 cm. Thus, those 4 faces have a total area of ...

  (5 cm)(7.8 cm) = 39.0 cm^2

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The two trapezoidal faces each have bases of length 1 and 2 cm, and a "height" of 2.3 cm. Together, their areas are ...

  A = 2×(1/2)(b1 +b2)h = (b1 +b2)h

  A = (1 cm +2 cm)(2.3 cm) = 6.9 cm^2

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The surface area of the entire trapezoidal prism is then ...

  total area = base area + lateral area = 6.9 cm^2 +39 cm^2

  total area = 45.9 cm^2

The student's answer of 57.4 cm^2 is not correct. (We don't know where that calculation came from.)