TAILIEUCHUNG - – THE GRE QUANTITATIVE SECTION – The area of a sector is found in a similar way to finding the

– 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, simx ply multiply the area of a circle, πr2, by the fraction 360 , again using x as the degree measure of the central angle. Example: Given x = 60º and r = 8, find the area of the sector: r o r x A= A= A= A= 60 360 1 6 64 6( 32 2( ( )82 64( ) ) ) Polygons and Parallelograms A polygon is a closed figure with three or more sides. B C A D F E T ERMS. | 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 of the exterior angles of any polygon equals 360 degrees. 192 THE GRE QUANTITATIVE SECTION Similar Polygons If two polygons are similar their corresponding angles are equal and the ratio of the corresponding sides is in proportion. Example These two polygons are similar because their angles are equal and the ratio of the corresponding sides is in proportion. Parallelograms A parallelogram is a quadrilateral with two pairs of parallel sides. In this figure AB II CD and BC II AD. A parallelogram has the following characteristics Opposite sides are equal AB CD and BC AD . Opposite angles are equal mZA mZC .

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