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

# Properties of Squares

How many sides of a square have equal length?

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 $$PQRS$$.

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 $$BEFC$$?

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