ISO trapezoid v2

bases of Isosceles trapezoid measured 20 cm and 4 cm and its perimeter is 55 cm. What is the are of a trapezoid?

Correct answer:

S =  159.31 cm²

Step-by-step explanation:

$$\begin{gathered} a=20\text{ cm } \\ b=4\text{ cm } \\ o=55\text{ cm } \\ o=a+b+2r \\ r={\displaystyle \frac{o-a-b}{2}}={\displaystyle \frac{55-20-4}{2}}={\displaystyle \frac{31}{2}}=15.5\text{ cm } \\ x={\displaystyle \frac{\mathrm{\mid }a-b\mathrm{\mid }}{2}}={\displaystyle \frac{\mathrm{\mid }20-4\mathrm{\mid }}{2}}=8\text{ cm } \\ h=\sqrt{r^2-x^2}=\sqrt{15.5^2-8^2}\doteq 13.2759\text{ cm } \\ S={\displaystyle \frac{a+b}{2}}\cdot h={\displaystyle \frac{20+4}{2}}\cdot 13.2759=6\sqrt{705}=159.31{\text{cm}}^2 \end{gathered}$$

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