**Quadrilaterals**

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* = 2*w* + 2*l*.

*A* = l•*w*

*P *= 2*w* + 2*l*

**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).

*A*=

*s*

^{2}and its perimeter is

*P*= 4

*s*, where s is the length of a side:

*A*=

*s*

^{2}

*P*= 4

*s*

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:

*A*=$\left(\frac{{b}_{1}+{b}_{2}}{2}\right)$*h*