Determine the area

Determine the area of the trapezoid ABCD, in which the following holds: AB= 6cm, Area of triangle ABC= 15 cm², area of triangle BCD= 20 cm², AB||CD.

Final Answer:

S =  35 cm²

Step-by-step explanation:

$$\begin{gathered} a=6\text{cm} \\ {S}_1=15{\text{cm}}^2 \\ {S}_2=20{\text{cm}}^2 \\ {S}_1=\frac{a\cdot h}{2} \\ h=\frac{2\cdot S_1}{a}=\frac{2\cdot 15}{6}=5\text{cm} \\ {S}_2=\frac{c\cdot h}{2} \\ c=\frac{2\cdot S_2}{h}=\frac{2\cdot 20}{5}=8\text{cm} \\ S=\frac{a+c}{2}\cdot h=\frac{6+8}{2}\cdot 5=35{\text{cm}}^2 \end{gathered}$$

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