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Question Number 11632 by Joel576 last updated on 29/Mar/17

Answered by sandy_suhendra last updated on 29/Mar/17

Commented by sandy_suhendra last updated on 29/Mar/17

$$\mathrm{Area}\mathrm{\Delta }\mathrm{AOB}+\mathrm{Area}\mathrm{\Delta }\mathrm{BPC}$$$$=\frac{\mathrm{AB}\times \frac{1}{2}\mathrm{CD}}{2}+\frac{\mathrm{BC}\times \frac{1}{2}\mathrm{CD}}{2}$$$$=\frac{1}{4}\mathrm{AB}\times \mathrm{CD}+\frac{1}{4}\mathrm{BC}\times \mathrm{CD}$$$$=\frac{1}{4}\mathrm{CD}\times (\mathrm{AB}+\mathrm{BC})$$$$=\frac{1}{4}\mathrm{CD}\times \mathrm{AC}=\frac{1}{4}\times 50\times 200$$$$=2,500$$$$$$$$\mathrm{A}\mathrm{\Delta }\mathrm{AEC}=\frac{\mathrm{AC}\times \mathrm{CD}}{2}=\frac{200\times 50}{2}$$$$=5,000$$$$$$$$\mathrm{A}\mathrm{shaded}=\mathrm{A}\mathrm{\Delta }\mathrm{AEC}-(\mathrm{A}\mathrm{\Delta }\mathrm{AOB}+\mathrm{A}\mathrm{\Delta }\mathrm{BPC})$$$$=5,000-2,500=2,500$$

Commented by Joel576 last updated on 29/Mar/17

$$\mathrm{but}\mathrm{AC}=200$$

Commented by sandy_suhendra last updated on 29/Mar/17

$$\mathrm{oh}\mathrm{sorry},\mathrm{I}\mathrm{have}\mathrm{fixed}\mathrm{it}$$

Commented by Joel576 last updated on 29/Mar/17

$$\mathrm{no}\mathrm{problem},\mathrm{thank}\mathrm{you}\mathrm{very}\mathrm{much}$$

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