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16 May 2024, 00:56
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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100% (00:38) correct
0% (00:00) wrong based on 1 sessions
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In the rectangular solid above, TU=3, UV=4, and VR=2. What is the area of the shaded rectangular region?
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19 May 2024, 12:07
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Here we have in the rectangle RSTV the side RS = 2 and VT is the hypotenuse of the right triangle VTU where TU = 3 and UV = 4.
By Pythagoras theorem for right triangle we know that
VT = \(\sqrt{3^2 + 4^2}\) =5
So the Area of the shaded region = \(2 * 5\)= 10.
By Pythagoras theorem for right triangle we know that
VT = \(\sqrt{3^2 + 4^2}\) =5
So the Area of the shaded region = \(2 * 5\)= 10.
28 Jul 2024, 11:08
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Official Explanation
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 RC 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 and UV=4, so TU=3 by the Pythagorean theorem you can conclude that
VT=\(\sqrt{3^2+4^2} =\sqrt{16+9} = \sqrt{25} = 5\). Therefore, the area of the shaded rectangular region is (5)(2) = 10. The correct answer is 10.
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 RC 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 and UV=4, so TU=3 by the Pythagorean theorem you can conclude that
VT=\(\sqrt{3^2+4^2} =\sqrt{16+9} = \sqrt{25} = 5\). Therefore, the area of the shaded rectangular region is (5)(2) = 10. The correct answer is 10.
