Circles

This lessson is part of a series of lessons for the quantitative reasoning section of the GRE revised General Test. In this lesson, we will learn:

  • quadrilaterals; squares, rectangles, parallelograms, trapezoids
  • area of quadrilaterals

 

 

Circles

Every quadrilateral has four sides and four interior angles. The measures of the interior angles add up to 360°.

The following are special quadrilaterals.

• A quadrilateral with four right angles is called a rectangle. Opposite sides of a rectangle are parallel and congruent, and the two diagonals are also congruent.

rectangles

PQ = SR, PS = QR and PR = QS

• A rectangle with four congruent sides is called a square.

• A quadrilateral in which both pairs of opposite sides are parallel is called a parallelogram. In a parallelogram, opposite sides are congruent and opposite angles are congruent. Rectangles and squares are also parallelograms.

parallelogram

PQ = SR and PS = QR

• A quadrilateral in which two opposite sides are parallel is called a trapezoid.

trapezoid 2l is parallel to m

The following video shows how to classifying quadrilaterals based on the given information.

 

 

Area of Quadrilaterals

For all parallelograms, including rectangles and squares, the area A equals the product of the length of a base b and the corresponding height h; that is,

A = bh

Any side can be used as a base. The height corresponding to the base is the perpendicular line segment from any point of a base to the opposite side (or an extension of that side).

Below are examples of finding the areas of a square, a rectangle and a parallelogram.

area

 

The area A of a trapezoid equals half the product of the sum of the lengths of the two parallel sides a and b and and the corresponding height h; that is,

trapezoid area formula

Area of trapezoid

 

This video gives formulas and examples for how to find the area of squares, rectangles, triangles, parallelograms, and trapezoids. The video also explains the difference between base and height.

 

 

 

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