Trapezoid perimeter base

An isosceles trapezoid has one base twice as short as the other. Its area is 42 cm², and its height is 4 cm. Calculate its circumference if you know that the arm is 5.3 cm long.

Final Answer:

o =  31.6 cm

Step-by-step explanation:

$$\begin{gathered} r=5.3\text{cm} \\ S=42{\text{cm}}^2 \\ h=4\text{cm} \\ a=2c \\ S=\frac{a+c}{2}\cdot h \\ S=\frac{2c+c}{2}\cdot h \\ S=\frac{3c}{2}\cdot h \\ c=\frac{2\cdot S}{3\cdot h}=\frac{2\cdot 42}{3\cdot 4}=7\text{cm} \\ a=2\cdot c=2\cdot 7=14\text{cm} \\ o=a+c+2\cdot r=14+7+2\cdot 5.3=31.6\text{cm} \end{gathered}$$

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