In 1800 the area of the united states was 891,364 square miles after the louisiana purchase in 1803 the area increased by about 93% what was the area of united states after the louisiana purchase round to the nearest square mile

891,364 + 0.93(891,364 ) =
891,364 + 828968.52 =
1,720,332.52 rounded = 1,720,333 sq miles <==

1) Given
2) Adding segments AB and BC together gives AC (Addition postulate, not too sure about the terminology) 
3) Segment Addition postulate 
4) Segment Addition postulate(Knowing that AC=BD, the distance between BC and CD add up to BD, shown in #3. AB and BC add together to give AC) 
5) Subtraction property of Equality 

Hope I helped :)