Isosceles trapezoid

The bases of the isosceles trapezoid are in the ratio of 5:3. The arms have a length of 5 cm and height = 4.8 cm. Calculate the circumference and area of a trapezoid.

Final Answer:

o =  21.2 cm
S =  26.88 cm²

Step-by-step explanation:

$$\begin{gathered} r=5\text{cm} \\ v=4.8\text{cm} \\ {x}^2+v^2=r^2=5^2=25 \\ x=\sqrt{r^2-v^2}=\sqrt{5^2-4.8^2}=\frac{7}{5}=1.4\text{cm} \\ 3\cdot a=5\cdot c \\ x=(a-c)/2 \\ 3\cdot a=5\cdot c \\ 1.4=(a-c)/2 \\ 3a-5c=0 \\ a-c=2.8 \\ Row2-\frac{1}{3}\cdot Row1\to Row2 \\ 3a-5c=0 \\ 0.67c=2.8 \\ c=\frac{2.8}{0.66666667}=4.2 \\ a=\frac{0+5c}{3}=\frac{0+5\cdot 4.2}{3}=7 \\ a=7 \\ c=\frac{21}{5}=4.2 \\ o=a+c+2\cdot r=7+4.2+2\cdot 5=21.2\text{cm} \end{gathered}$$

$S=\frac{a+c}{2}\cdot v=\frac{7+4.2}{2}\cdot 4.8=\frac{672}{25}{\text{cm}}^2=26.88{\text{cm}}^2$

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