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Directions: Your answer may be an integer, a decimal, or a fraction, and it may be negative. Enter the exact answer unless the question asks you to round your answer.
Q. In the rectangular solid above, TU = 3, UV = 4, and VR = 2. What is the area of the shaded rectangular region?
Correct answer is '10'. Can you explain this answer?
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Directions: Your answer may be an integer, a decimal, or a fraction, ...
To find the area of the shaded rectangular region, you need to multiply the length of the rectangular region by its width. In this question you are given the lengths of three edges: TU = 3, UV = 4, and VR = 2. Note that VR is the length of the shaded rectangle. To find the width of the shaded rectangle, you need to find either RS or VT. Note that VT lies on the front face of the rectangular solid. It is the hypotenuse of right triangle VUT. You know that UV = 4 and TU = 3, so by the Pythagorean theorem you can conclude that VT = √32 + 42 = √9 + 16 = 25 = 5. Therefore, the area of the shaded rectangular region is (5)(2) = 10. The correct answer is 10.
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Directions: Your answer may be an integer, a decimal, or a fraction, ...
To find the area of the shaded rectangular region, you need to multiply the length of the rectangular region by its width. In this question you are given the lengths of three edges: TU = 3, UV = 4, and VR = 2. Note that VR is the length of the shaded rectangle. To find the width of the shaded rectangle, you need to find either RS or VT. Note that VT lies on the front face of the rectangular solid. It is the hypotenuse of right triangle VUT. You know that UV = 4 and TU = 3, so by the Pythagorean theorem you can conclude that VT = √32 + 42 = √9 + 16 = 25 = 5. Therefore, the area of the shaded rectangular region is (5)(2) = 10. The correct answer is 10.
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Directions: Your answer may be an integer, a decimal, or a fraction, and it may be negative. Enter the exact answer unless the question asks you to round your answer.Q. In the rectangular solid above, TU = 3, UV = 4, and VR = 2. What is the area of the shaded rectangular region?Correct answer is '10'. Can you explain this answer?
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