Rectangular trapezoid

The ABCD rectangular trapezoid with the AB and CD bases is divided by the diagonal AC into two equilateral rectangular triangles. The length of the diagonal AC is 62cm. Calculate the trapezium area in cm square and calculate how many different perimeters of the ABC and ACD triangles are in centimeters.

Correct answer:

S =  2883 cm²
x =  62 cm

Step-by-step explanation:

$$\begin{gathered} u=62\text{cm} \\ a=\sqrt{u^2+u^2}=\sqrt{62^2+62^2}=62\sqrt{2}\text{cm}\doteq 87.6812\text{cm} \\ {c}^2+c^2=u^2 \\ c=u/\sqrt{2}=62/\sqrt{2}=31\sqrt{2}\text{cm}\doteq 43.8406\text{cm} \\ S=\frac{a+c}{2}\cdot c=\frac{87.6812+43.8406}{2}\cdot 43.8406=2883{\text{cm}}^2 \end{gathered}$$

$$\begin{gathered} o_1=2\cdot c+u=2\cdot 43.8406+62\doteq 149.6812\text{cm} \\ {o}_2=2\cdot u+a=2\cdot 62+87.6812\doteq 211.6812\text{cm} \\ x=o_2-o_1=211.6812-149.6812=62\text{cm} \end{gathered}$$

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