Isosceles trapezoid

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

Correct result:

o =  21.2 cm
S =  26.88 cm²

Solution:

$$\begin{gathered} r=5\text{ cm } \\ v=4.8\text{ cm } \\ {x}^2+v^2=r^2=5^2=25 \\ x=\sqrt{r^2-v^2}=\sqrt{5^2-4.8^2}={\displaystyle \frac{7}{5}}=1.4\text{ cm } \\ 3\cdot a=5\cdot c \\ x=(a-c)\mathrm{/}2 \\ 3\cdot a=5\cdot c \\ 1.4=(a-c)\mathrm{/}2 \\ 3a-5c=0 \\ a-c=2.8 \\ a=7 \\ c={\displaystyle \frac{21}{5}}=4.2 \\ o=a+c+2\cdot r=7+4.2+2\cdot 5={\displaystyle \frac{106}{5}}={\displaystyle \frac{106}{5}}\text{ cm}=21.2\text{ cm} \end{gathered}$$

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

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