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Quadrilaterals

These shapes have four sides and 360° of interior angle goodness.

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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