Rectangular trapezoid

The rectangular trapezoid ABCD is: /AB/ = /BC/ = /AC/. The length of the median is 6 cm. Calculate the circumference and area of a trapezoid.

Correct result:

o =  26.928 cm
S =  41.569 cm2

Solution:

s=6 s=(a+c)/2  c=a/2 6=(a+a/2)/2 a=12/(1+1/2)=8  b=a=8 c=a/2=8/2=4 d=a2−(a/2)2=82−(8/2)2≐4 3≐6.9282 o=a+a+c+d=8+8+4+6.9282=26.928 cms=6 \ \\ s=(a+c)/2 \ \\ \ \\ c=a/2 \ \\ 6=(a+a/2)/2 \ \\ a=12 / (1+1/2)=8 \ \\ \ \\ b=a=8 \ \\ c=a/2=8/2=4 \ \\ d=\sqrt{ a^2-(a/2)^2 }=\sqrt{ 8^2-(8/2)^2 } \doteq 4 \ \sqrt{ 3 } \doteq 6.9282 \ \\ o=a+a+c+d=8+8+4+6.9282=26.928 \ \text{cm}
S=d⋅ s=6.9282⋅ 6=24 3=41.569 cm2S=d \cdot \ s=6.9282 \cdot \ 6=24 \ \sqrt{ 3 }=41.569 \ \text{cm}^2

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