MathDB
Area of Triangle

Source:

January 11, 2009
geometryratioanalytic geometryPythagorean Theoremarea of a triangleHeron's formula

Problem Statement

Let line AC AC be perpendicular to line CE CE. Connect A A to D D, the midpoint of CE CE, and connect E E to B B, the midpoint of AC AC. If AD AD and EB EB intersect in point F F, and \overline{BC} \equal{} \overline{CD} \equal{} 15 inches, then the area of triangle DFE DFE, in square inches, is: <spanclass=′latex−bold′>(A)</span> 50<spanclass=′latex−bold′>(B)</span> 502<spanclass=′latex−bold′>(C)</span> 75<spanclass=′latex−bold′>(D)</span> 152105<spanclass=′latex−bold′>(E)</span> 100 <span class='latex-bold'>(A)</span>\ 50 \qquad <span class='latex-bold'>(B)</span>\ 50\sqrt {2} \qquad <span class='latex-bold'>(C)</span>\ 75 \qquad <span class='latex-bold'>(D)</span>\ \frac {15}{2}\sqrt {105} \qquad <span class='latex-bold'>(E)</span>\ 100
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