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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 x w and its perimeter is P = 2w + 2l.

In the figure, what is the perimeter of the pentagon?

  1. 12
  2. 13
  3. 17
  4. 20
  5. 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:

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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