Answer:
9
Explanation:
You want the length of the median of an isosceles trapezoid with sides in the ratios 2:1:1:1 and an area of 27√3 square units.
Equilateral triangle
The area of an equilateral triangle is ...
A = (√3/4)s² . . . . . s = side length
Figure area
The area of the described figure (shown in the attachment) is that of 3 equilateral triangles. The side lengths of those can be found from ...
A = 3·(√3/4)s²
27√3 = (3/4)√3s²
4/3(27) = s² = 36
s = 6
Median
The median is the average of the two base lengths:
m = (1 + 2)/2 · s = 3/2(6)
m = 9
The length of the median of the trapezoid is 9 units.
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