Circumference 66134

The isosceles trapezoid ABCD has an area of 36 cm2. One of its bases is two times longer than the other. Height is 4 cm. Calculate the circumference of the trapezoid.

Correct answer:

o =  28 cm

Step-by-step explanation:

S=36 cm2 h=4 cm  a=2c S=(a+c)/2⋅ h a=2c 36=(a+c)/2⋅ 4  a=2⋅ c 36=(a+c)/2⋅ 4  a−2c=0 4a+4c=72  Pivot:Row1↔Row2 4a+4c=72 a−2c=0  Row2−41​⋅ Row1→Row2 4a+4c=72 −3c=−18  c=−3−18​=6 a=472−4c​=472−4⋅ 6​=12  a=12 c=6  x2 = h2 + ((a−c)/2)2 x=h2+((a−c)/2)2​=42+((12−6)/2)2​=5 cm  o=a+c+x+x=12+6+5+5=28=28 cm   Verifying Solution:   S1​=2a+c​⋅ h=212+6​⋅ 4=36 cm2

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