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09 May 2021, 11:40
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Difficulty:
65%
(hard)
Question Stats:
44% (04:08) correct
56%
(03:19)
wrong
based on 9
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The figure above is composed of a triangle and a trapezoid and has perimeter 18cm. What is its total area?
A. \(\frac{21\sqrt{3}}{2}\)
B. \(\frac{23\sqrt{3}}{2}\)
C. \(\frac{25\sqrt{3}}{2}\)
D. \(\frac{27\sqrt{3}}{2}\)
E. \(\frac{29\sqrt{3}}{2}\)
10 May 2021, 00:56
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nick1816
Increase EC and DB to meet at A.
If we add the perimeter, we get x=2 as shown in the sketch.
I. If you were able to convert the trapezium to an equilateral triangle, you could find area as below
Now triangle ADE and DEF are equilateral triangle as all angles are 60, and both are congruent as the sides are 3+x or 3+2=5.
Area of ADE=Area of DEF = \(\frac{\sqrt{3}*5^2}{4}\)
Area of ABC = \(\frac{\sqrt{3}*2^2}{4}\)
Area of BCEFD = Area of ADE + Area of DEF - Area of ABC =\(2* \frac{\sqrt{3}*5^2}{4}-\frac{\sqrt{3}*2^2}{4}=\frac{\sqrt{3}*46}{4}\)
\(\frac{\sqrt{3}*23}{2}\)
II. If you were not able to convert the trapezium to an equilateral triangle, you could find area of trapezium as below
You could also find Area of trapezium BCDE as the height GC can be found from triangle CEG, which is a 30-60-90 triangle, so GC = \(\frac{3\sqrt{3}}{2}\)
Area = \(\frac{2+5}{2}*\frac{3\sqrt{3}}{2}=\frac{21\sqrt{3}}{4}\)
Area of BCEFD = Area of DEF + Area of BCDE =\( \frac{\sqrt{3}*5^2}{4}+\frac{\sqrt{3}*21}{4}=\frac{\sqrt{3}*46}{4}\)
\(\frac{\sqrt{3}*23}{2}\)
Attachments
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