What is the perimeter of the trapezoid shown?

The altitude = √3.....So ...we have a 1 - √3 - 2  triangle formed by this altitude and the side of 2. The other side of the triangle between where the altitude intersects the base and the side of 2 equals 1.

So...by symmetry, the base = 1 + 2 + 1 = 4

So..the perimeter is  2 + 2 + 2 + 4 =  10

If you extend the sloping sides of the trapezoid upwards, you would see two equilateral triangles, one inside the other.  Because both triangles are equilateral the sides of the smaller triangle are all of size 2, which means the sides of the larger one are all 4.  This means the perimeter of the trapezoid shown is 4 + 2*3 = 10.

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