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

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

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

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