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SAT Math: Angles and Polygons 03

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The figure above shows a regular hexagon with sides of length a and a square with sides of length a. If the area of the hexagon is 216 \sqrt{3} square inches, what is the area, in square inches, of the square?

In triangle LNP above, LN=LP, M is the midpoint of LN, and O is the midpoint of LP. If LM = x, and MO = 4, what is the length of NP?

In the figure above, JL is congruent to JK. If the measurement of \angle MLJ is 115 \textdegree, what is the measurement of angle J?
The lengths of the sides of a triangle are x, 16, and 31, where x is the shortest side. If the triangle is not isosceles, what is a possible value of x?


In the figure above, AB=4, CD=18, BC=12. What is the value of DE?


 

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