MathDB

21

Part of 2012 AMC 10

Problems(2)

3D Geometry Area

Source: 2012 AMC10A Problem #21

2/8/2012
Let points A=(0,0,0)A=(0,0,0), B=(1,0,0)B=(1,0,0), C=(0,2,0)C=(0,2,0), and D=(0,0,3)D=(0,0,3). Points E,F,GE,F,G, and HH are midpoints of line segments BD‾,AB‾,AC‾\overline{BD},\overline{AB},\overline{AC}, and DC‾\overline{DC} respectively. What is the area of EFGHEFGH?
<spanclass=′latex−bold′>(A)</span> 2<spanclass=′latex−bold′>(B)</span> 253<spanclass=′latex−bold′>(C)</span> 354<spanclass=′latex−bold′>(D)</span> 3<spanclass=′latex−bold′>(E)</span> 273 <span class='latex-bold'>(A)</span>\ \sqrt2 \qquad<span class='latex-bold'>(B)</span>\ \frac{2\sqrt5}{3} \qquad<span class='latex-bold'>(C)</span>\ \frac{3\sqrt5}{4} \qquad<span class='latex-bold'>(D)</span>\ \sqrt3 \qquad<span class='latex-bold'>(E)</span>\ \frac{2\sqrt7}{3}
geometryvectorrectangletrigonometryAMC
Four Points in a Plane

Source: 2012 AMC 10B Problem #21

2/23/2012
Four distinct points are arranged in a plane so that the segments connecting them has lengths a,a,a,a,2a,a,a,a,a,2a, and bb. What is the ratio of bb to aa?
<spanclass=′latex−bold′>(A)</span> 3<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 5<spanclass=′latex−bold′>(D)</span> 3<spanclass=′latex−bold′>(E)</span> π <span class='latex-bold'>(A)</span>\ \sqrt{3}\qquad<span class='latex-bold'>(B)</span>\ 2\qquad<span class='latex-bold'>(C)</span>\ \sqrt{5}\qquad<span class='latex-bold'>(D)</span>\ 3\qquad<span class='latex-bold'>(E)</span>\ \pi
ratioinequalitiestriangle inequalityAMC