Isosceles

Isosceles trapezium ABCD ABC = 12 angle ABC = 40 ° b=6. Calculate the circumference and area.

Correct answer:

o =  26.8075
S =  28.5542

Step-by-step explanation:

$$\begin{gathered} a=12 \\ b=6 \\ B=40^{\circ } \\ x=b\cdot \cos B^{\circ }=b\cdot \cos 40^{\circ }=6\cdot \cos 40^{\circ }=6\cdot 0.766044=4.59627 \\ c=a-2\cdot x=12-2\cdot 4.5963\doteq 2.8075 \\ o=a+2\cdot b+c=12+2\cdot 6+2.8075=26.8075 \end{gathered}$$

$$\begin{gathered} h=b\cdot \sin B^{\circ }=b\cdot \sin 40^{\circ }=6\cdot \sin 40^{\circ }=6\cdot 0.642788=3.85673 \\ S={\displaystyle \frac{a+c}{2}}\cdot h={\displaystyle \frac{12+2.8075}{2}}\cdot 3.8567=28.5542 \end{gathered}$$

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