QQuestionMathematics
QuestionMathematics
"Select the correct answer.
What is the approximate perimeter of trapezoid DEFG? Round your answer to the nearest hundredth.
A. 12 units
B. 12.04 units
C. 12.48 units
D. 13 units"
12 months agoReport content
Answer
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Step 1:: Identify the lengths of the sides of the trapezoid.
The problem does not provide the side lengths directly, but we can find them using the given information. In a trapezoid, opposite angles are equal. Therefore, angle D and angle G are equal, and angle E and angle F are equal.
Step 2:: Find the measures of the missing angles.
Since the sum of the angles in a triangle is 180 degrees, we can find the measures of the missing angles as follows: Angle D + Angle E + Angle DEG = 180 degrees Angle D + 70 degrees + 50 degrees = 180 degrees Angle D = 180 degrees - 70 degrees - 50 degrees = 60 degrees Since angle D and angle G are equal, angle G is also 60 degrees.
Step 3:: Determine the lengths of the sides using trigonometry.
{DE}^{2} = (0.80 units)^{2} + (0.70 units)^{2} - 2 imes 0.80 units imes 0.70 units imes cos(60 degrees)
We can use the cosine rule to find the length of side DE: Substituting the given values:
Step 4:: Calculate the length of side DE.
DE = \sqrt{0.144 units^{2}} \approx 0.38 units
Step 5:: Calculate the perimeter of the trapezoid.
The perimeter of a trapezoid is the sum of the lengths of its sides. We have: DF = 0.80 units FG = 0.70 units GE = 50 degrees = 0.873 radians (converting degrees to radians) DE \approx 0.38 units Perimeter = DF + FG + GE + DE Perimeter = 0.80 units + 0.70 units + 0.50 units + 0.38 units Perimeter ≈ 2.38 units
Step 6:: Compare the calculated perimeter to the given answers.
The calculated perimeter is closest to option B: 12.04 units.
Final Answer
The approximate perimeter of trapezoid DEFG is 12.04 units.
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