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The ratio of the four sides of a trapezoid is $2:1:1:1. $ the area of the trapezoid is $27\sqrt 3. $ find the length of the median of the trapezoid

User OARP
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1 Answer

1 vote

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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The ratio of the four sides of a trapezoid is $2:1:1:1. $ the area of the trapezoid-example-1
User Arnaud Bouchot
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