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Properties of Squares


True or False?

Connecting the midpoints of the four sides of any simple quadrilateral makes a parallelogram.

Square \(ABCD\) has side length equal to \(12\). \(E\) is the midpoint of \(AD\) and \(F\) is the midpoint of \(DC\). What is the area of quadrilateral \(BEFC\)?

\(ABCD\) is a square such that \( [ABCD] = 120 \). \(E, F, G, H\) are the midpoints of \( AB, BC, CD\) and \(DA\) respectively. What is \( [EFGH] \)?

Details and assumptions

\([PQRS] \) denotes the area of figure \(PQRS\).

Square \(ABCD\) has \(M\) as the midpoint of \(AB\), \(N\) as the midpoint of \(BC\), \(P\) as the midpoint of \(CD\) and \(Q\) as the midpoint of \(MP\). If \([AMNPDQ] = 50\), what is the value of \([ABCD]\)?

Details and assumptions

\([PQRS]\) refers to the area of figure \(PQRS\).

How many sides of a square have equal length?


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