Through-the-vertices-of-the-smaller-base-AB-of-the-trapezoid-ABCD-two-parallel-lines-are-drawn-intersecting-the-segment-CD-These-lines-and-the-trapezoid-s-diagonals-divide-it-into-seven-triangles-an

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Question Number 16947 by Tinkutara last updated on 28/Jun/17

$$\mathrm{Through}\mathrm{the}\mathrm{vertices}\mathrm{of}\mathrm{the}\mathrm{smaller}$$$$\mathrm{base}AB\mathrm{of}\mathrm{the}\mathrm{trapezoid}ABCD\mathrm{two}$$$$\mathrm{parallel}\mathrm{lines}\mathrm{are}\mathrm{drawn},\mathrm{intersecting}$$$$\mathrm{the}\mathrm{segment}CD.\mathrm{These}\mathrm{lines}\mathrm{and}\mathrm{the}$$$${\mathrm{trapezoid}}^{\prime }\mathrm{s}\mathrm{diagonals}\mathrm{divide}\mathrm{it}\mathrm{into}$$$$\mathrm{seven}\mathrm{triangles}\mathrm{and}\mathrm{a}\mathrm{pentagon}.\mathrm{Show}$$$$\mathrm{that}\mathrm{the}\mathrm{area}\mathrm{of}\mathrm{the}\mathrm{pentagon}\mathrm{equals}$$$$\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{the}\mathrm{areas}\mathrm{of}\mathrm{the}\mathrm{three}$$$$\mathrm{triangles}\mathrm{that}\mathrm{share}\mathrm{a}\mathrm{common}\mathrm{side}$$$$\mathrm{with}\mathrm{the}\mathrm{trapezoid}.$$

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