Tham khảo tài liệu 'the gre quatitative section 1', ngoại ngữ, anh ngữ phổ thông phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | THE GRE QUANTITATIVE SECTION A central angle of a circle is an angle that has its vertex at the center and that has sides that are radii. Central angles have the same degree measure as the arc it forms. Length of Arc To find the length of an arc multiply the circumference of the circle 2nr where r the radius of the circle by the fraction 360 where x is the degree measure of the arc or central angle of the arc. Example Find the length of the arc if x 36 and r 70. L H0 X 2 n 70 L -j0 X 140n L 14n Area of a Sector A sector of a circle is a region contained within the interior of a central angle and arc. 190 THE GRE QUANTITATIVE SECTION The area of a sector is found in a similar way to finding the length of an arc. To find the area of a sector simply multiply the area of a circle nr2 by the fraction 3600 again using x as the degree measure of the central angle. Example Given x 60 and r 8 find the area of the sector . 60 A Ho x H82 A I X 64 n- . 64 A 6 A f Polygons and Parallelograms A polygon is a closed figure with three or more sides. Terms Related to Polygons Vertices are corner points also called endpoints of a polygon. The vertices in the previous polygon are A B C D E and F. A diagonal of a polygon is a line segment between two nonadjacent vertices. The two diagonals indicated in the previous polygon are line segments BF and AE. A regular or equilateral polygon s sides are all equal. An equiangular polygon s angles are all equal. 191 THE GRE QUANTITATIVE SECTION Angles of a Quadrilateral A quadrilateral is a four-sided polygon. Since a quadrilateral can be divided by a diagonal into two triangles the sum of its angles will equal 180 180 360 degrees. mZ1 mZ2 mZ3 mZ4 360 Interior Angles To find the sum of the interior angles of any polygon use this formula s 180 x - 2 where x is the number of polygon sides. Example Find the sum of the angles in the following polygon. s 5 - 2 X 180 s 3 X 180 s 540 Exterior Angles Similar to the exterior angles of a triangle the sum
