Rectangular trapezoid

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

Final Answer:

o =  26.9282 cm
S =  41.5692 cm²

Step-by-step explanation:

$$\begin{gathered} s=6\text{cm} \\ s=(a+c)/2 \\ c=a/2 \\ 6=(a+a/2)/2 \\ a=12/(1+1/2)=8\text{cm} \\ b=a=8\text{cm} \\ c=a/2=8/2=4\text{cm} \\ {a}^2=d^2+(a/2{)}^2 \\ d=\sqrt{a^2-(a/2{)}^2}=\sqrt{8^2-(8/2{)}^2}=4\sqrt{3}\text{cm}\doteq 6.9282\text{cm} \\ o=a+a+c+d=8+8+4+6.9282=26.9282\text{cm} \end{gathered}$$

$S=d\cdot s=6.9282\cdot 6=24\sqrt{3}=41.5692{\text{cm}}^2$

Try another example