Trapezoid complete

Calculate side b and the height of the trapezoid if a = 5.1 cm; c = 6.8 cm; d = 4.7 cm; circumference is 21 cm, and the area is 17.85 cm².

Final Answer:

b =  4.4 cm
v =  3 cm

Step-by-step explanation:

$$\begin{gathered} a=5.1\text{cm} \\ c=6.8\text{cm} \\ d=4.7\text{cm} \\ o=21\text{cm} \\ S=17.85{\text{cm}}^2 \\ o=a+b+c+d \\ b=o-a-c-d=21-5.1-6.8-4.7=4.4\text{cm} \end{gathered}$$

$$\begin{gathered} S=\frac{a+c}{2}\cdot v \\ v=\frac{2\cdot S}{a+c}=\frac{2\cdot 17.85}{5.1+6.8}=3\text{cm} \end{gathered}$$

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