Calculate trapezoid

A trapezoid is given: c = 4.2 cm, h = 8 cm, S = 42.4 cm, d = 8.4
It would help if you calculated the following: sides a and b, and perimeter o:

Final Answer:

a =  6.4 cm
b =  8.0082 cm
o =  27.0082 cm

Step-by-step explanation:

$$\begin{gathered} c=4.2 \\ v=8 \\ S=42.4 \\ d=8.4 \\ a=2\cdot S/v-c=2\cdot 42.4/8-4.2=6.4\text{cm} \end{gathered}$$

$$\begin{gathered} x=\sqrt{d^2-v^2}=\sqrt{8.4^2-8^2}\doteq 2.5612 \\ y=a-c-x=6.4-4.2-2.5612\doteq -0.3612 \\ b=\sqrt{v^2+y^2}=\sqrt{8^2+(-0.3612{)}^2}=8.0082\text{cm} \end{gathered}$$

$o=a+b+c+d=6.4+8.0082+4.2+8.4=27.0082\text{cm}$

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