The bases

The bases of the isosceles trapezoid ABCD have 10 cm and 6 cm lengths. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and area of the ABCD trapezoid.

Correct answer:

o =  22.2229 cm
S =  19.0681 cm²

Step-by-step explanation:

$$\begin{gathered} a=10\text{cm} \\ c=6\text{cm} \\ \alpha =50{}^{\circ } \\ x=(a-c)/2=(10-6)/2=2\text{cm} \\ \cos \alpha =x:r \\ r=x/\cos (\alpha )=2/\cos (50°)=3.11145\text{cm} \\ o=a+c+2\cdot r=10+6+2\cdot 3.1114=22.2229\text{cm} \end{gathered}$$

$$\begin{gathered} \tan \alpha =h:x \\ h=x\cdot \tan (\alpha )=2\cdot \tan (50°)=2.38351\text{cm} \\ S=\frac{a+c}{2}\cdot h=\frac{10+6}{2}\cdot 2.3835=19.0681{\text{cm}}^2 \end{gathered}$$

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