The isosceles

The isosceles trapezoid ABCD has bases of 18 cm and 12 cm. The angle at apex A is 60°. What is the circumference and content of the trapezoid?

Correct answer:

o =  42 cm
S =  77.9423 cm²

Step-by-step explanation:

$$\begin{gathered} a=18\text{ cm } \\ c=12\text{ cm } \\ \alpha =60\text{ ° } \\ x=(a-c)\mathrm{/}2=(18-12)\mathrm{/}2=3 \\ \cos \alpha =x:b \\ b=x\mathrm{/}\cos \alpha \mathrm{°}=x\mathrm{/}\cos 60\mathrm{°}=3\mathrm{/}\cos 60\mathrm{°}=3\mathrm{/}0.5=6\text{ cm } \\ d=b=6\text{ cm } \\ o=a+b+c+d=18+6+12+6=42\text{ cm} \end{gathered}$$

$$\begin{gathered} h=b\cdot \sin \alpha \mathrm{°}=b\cdot \sin 60\mathrm{°}=6\cdot \sin 60\mathrm{°}=6\cdot 0.866025=5.19615\text{ cm } \\ S={\displaystyle \frac{a+c}{2}}\cdot h={\displaystyle \frac{18+12}{2}}\cdot 5.1962=45\sqrt{3}=77.9423{\text{cm}}^2 \end{gathered}$$

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