# In the figure AD PARALLEL TO CD AD PERPENDICULAR TO AB .CB:17cm, AB:35cm, CD:27cm . find the area of shaded region .

$AB\;parallel\;to\;CD.\\*AB\;perpendicular\;to\;AD.\\*It\;is\;a\;trapezium.\\* Length\;of\;parallel\;sides\;are-AB=35\;cm,\;CD=27\;cm\\*Height\;of\; trapezium=AD=CE\\*CE\;is\;perpendicular\;to\;AB.\\*So,\;CE,\;EB\;and\;BC\; form\;a\;right-angled\;triangle.\\*So,\;BC^2=CE^2+EB^2\\*\Rightarrow BC^2=CE^2+(AB-AE)^2 \\* \Rightarrow BC^2=CE^2+(AB-CD)^2, \:\; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \;\because (AE=CD)\\*\Rightarrow 17^2=CE^2+(35-27)^2=CE^2+8^2\\* \Rightarrow CE^2=289-64=225\\* \Rightarrow CE=15\;cm\\*Area\;of\;trapezium=\frac{1}{2} \times height \times (sum\;of\;parallel\;sides)\\* \Rightarrow Area\;of\;trapezium=\frac{1}{2} \times 15 \times (35+27)\\* Area\;of\;trapezium=\frac{1}{2} \times 15 \times (62) = 465\;cm^2\\*$

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