Isosceles 5666

In the isosceles trapezoid ABCD, calculate the missing side length "a" and then its areas. Side b = d = 50 cm, c = 20 cm, height = 48 cm.

Correct answer:

a =  48 cm
S =  1632 cm²

Step-by-step explanation:

$$\begin{gathered} b=50\text{cm} \\ d=50\text{cm} \\ c=20\text{cm} \\ v=48\text{cm} \\ x=\sqrt{b^2-v^2}=\sqrt{50^2-48^2}=14\text{cm} \\ a=c+2\cdot x=20+2\cdot 14=48\text{cm} \end{gathered}$$

$S=(a+c)/2\cdot v=(48+20)/2\cdot 48=1632{\text{cm}}^2$

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