This is part of our
GRE Math Essentials project & GRE Math Essentials - A most comprehensive handout!!! that are the best complement to our
GRE Math Book. It provides a cutting-edge, in-depth overview of all the math concepts from basic to mid-upper levels. The book still remains our hallmark: from basic to the most advanced GRE math concepts tested during the exam. Moreover, the following chapters will give you many tips, tricks, and shortcuts to make your quant preparation more robust and solid.
Regular PolygonsA many sided closed figure is called a polygon. If all the sides of a polygon are equal, it is called a regular polygon.
1. Interior Angle + Exterior angle = 180°
2. \(P = n \times a\) (n = number of sides, a = side)
3. Sum of exterior angles \(= 360°\)
4. Sum of Interior angles \(= (2n – 4) 90°\)
5. Each Interior angle \(= [(\frac{2n – 4)}{n}] \times 90°\)
6. Each exterior angle \(= \frac{360}{n}\)
7.\( A = \frac{1}{2} P\)
\( r = \frac{1}{2 }\) n a r
P = perimeter (r = ⊥ from centre to any one side = radius of encircle)
Regular Hexagon1. Each interior angle = 120°
2. Sum of Interior angles = 720°
3. Each exterior angle = 60°
4. Area \(= (\frac{3\sqrt{3}}{2}) \times a^2 (a = side)\)
5. P = 6a
CircleA circle is the path traversed by a point which moves in such a way that its distance from a fixed point always remains constant.
C is called centre and R the radius of the circle. Circumference \(= 2 \pi R = \pi D\)
1. Area \(= A = \pi R^2 = \frac{\pi D^2}{4} (D = Diameter = 2R) \pi = \frac{22}{7} or 3.14\)
2. Length of arc of a circle is given by \(\ell (AB) = (\frac{θ°}{360°}) \times 2 \pi R\)
3. Area of Sector \(ABC = (\frac{θ}{360}) \times \pi R^2 = \frac{\frac{1}{2}}{(AB) \times R}\)
4. Distance travelled by a wheel in n revolutions \(= n\)\( \times\) circumference
5. Angle at the centre made by an arc = twice the angle made by the arc at any point on the remaining part of the circumference.
We have \(\angle APB =\frac{1}{2} \angle AOB = 30° = \angle AQB\)
6. Angle in a semicircle is a right angle.
Attachment:
GRE polygon.jpg [ 10.73 KiB | Viewed 5249 times ]
Attachment:
GRE circles.jpg [ 27.51 KiB | Viewed 5252 times ]
Attachment:
GRE circle (5).jpg [ 24.68 KiB | Viewed 5198 times ]
_________________