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A quadrilateral is a four-sided closed figure, where each side is a straight line.

The angle sum of a quadrilateral is 360°. You can view a quadrilateral as being composed of two 180- degree triangles:

A parallelogram is a quadrilateral in which the opposite sides are both parallel and congruent. Its area is base × height :

A = bh


The diagonals of a parallelogram bisect each other:


A parallelogram with four right angles is a rectangle. If w is the width and l is the length of a rectangle, then its area is A = l • w and its perimeter is P = 2w + 2l.

A = l•w
P = 2w + 2l


Example: In the figure below, what is the perimeter of the pentagon?

(A) 12
(B) 13
(C) 17
(D) 20
(E) 25

Add the following line to the figure:

Since the legs of the right triangle formed are of lengths 3 and 4, the triangle must be a 3-4-5 right triangle. Hence, the added line has length 5. Since the bottom figure is a rectangle, the length of the base of the figure is also 5. Hence, the perimeter of the pentagon is 3 + 4 + 4 + 5 + 4 = 20. The answer is (D).


If the opposite sides of a rectangle are equal, it is a square and its area is A = s2 and its perimeter is P = 4s, where s is the length of a side:

A = s2
P = 4s


The diagonals of a square bisect each other and are perpendicular to each other:

A quadrilateral with only one pair of parallel sides is a trapezoid. The parallel sides are called bases, and the non-parallel sides are called legs:

The area of a trapezoid is the average of the two bases times the height:



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