The gre quatitative section 2 docx

■ In a square, diagonals have both the same length and intersect at 90-degree angles. Solid Figures, Perimeter, and Area You will need to know some basic formulas for finding area, perimeter, and volume on the GRE. It is impor- tant that you can recognize the figures by their names and understand when to use which formula. To begin, it is necessary to explain five kinds of measurement: P ERIMETER The perimeter of an object is simply the sum of the lengths of all its sides. 6 7 4 10 Perimeter = 6 + 7 + 4 + 10 = 27 B C A D AC = DB and AC DB B C A D BD AC – THE GRE QUANTITATIVE SECTION– 195 AREA Area is the space inside of the lines defining the shape. You will need to know how to find the area of several geometric shapes and figures. The formulas needed for each are listed here: ■ To find the area of a triangle, use the formula A = ᎏ 1 2 ᎏ bh. ■ To find the area of a circle, use the formula A = ␲ r 2 . ■ To find the area of a parallelogram, use the formula A = bh. ■ To find the area of a rectangle, use the formula A = lw. ■ To find the area of a square, use the formula A = s 2 or A = ᎏ 1 2 ᎏ d 2 . w l h b r h b = Area – THE GRE QUANTITATIVE SECTION– 196 ■ To find the area of a trapezoid, use the formula A = ᎏ 1 2 ᎏ (b 1 + b 2 )h. V OLUME Volume is a measurement of a three-dimensional object such as a cube or a rectangular solid.An easy way to envi- sion volume is to think about filling an object with water.The volume measures how much water can fit inside. ■ To find the volume of a rectangular solid, use the formula V = lwh. ■ To find the volume of a cube, use the formula V = e 3 . e e = edge width length height h b 1 b 2 d s s s s – THE GRE QUANTITATIVE SECTION– 197 ■ To find the volume of a cylinder, use the formula V = ␲ r 2 h. SURFACE AREA The surface area of an object measures the combined area of each of its faces. The total surface area of a rec- tangular solid is double the sum of the area of the three different faces. For a cube, simply multiply the sur- face area of one of its sides by 6. ■ To find the surface area of a rectangular solid, use the formula A = 2(lw ϩ lh ϩ wh). ■ To find the surface area of a cube, use the formula A = 6e 2 . e e = edge V = lwh width length height 4 4 Surface area of front side = 16. Therefore, the surface area of the cube = 16 ϫ 6 = 96. r h – THE GRE QUANTITATIVE SECTION– 198 ■ To find the surface area of a right circular cylinder, use the formula A = 2 ␲ r 2 + 2 ␲ rh. CIRCUMFERENCE Circumference is the measure of the distance around a circle. ■ To find the circumference of a circle, use the formula C = 2 ␲ r. Coordinate Geometry Coordinate geometry is a form of geometrical operations in relation to a coordinate plane. A coordinate plane is a grid of square boxes divided into four quadrants by both a horizontal (x) and vertical (y) axis. These two axes intersect at one coordinate point—(0,0)—the origin. A coordinate pair, also called an ordered pair, is a specific point on the coordinate plane with the first number representing the horizontal placement and sec- ond number representing the vertical. Coordinate points are given in the form of (x,y). GRAPHING ORDERED PAIRS To graph ordered pairs, follow these guidelines: ■ The x-coordinate is listed first in the ordered pair and tells you how many units to move either to the left or to the right. If the x-coordinate is positive, move to the right. If the x-coordinate is negative, move to the left. ■ The y-coordinate is listed second and tells you how many units to move up or down. If the y-coordinate is positive, move up. If the y-coordinate is negative, move down. Example: Graph the following points: (–2,3), (2,3), (3,–2), and (–3,–2). Circumference – THE GRE QUANTITATIVE SECTION– 199 ■ Notice that the graph is broken into four quadrants with one point plotted in each one. Here is a chart to indicate which quadrants contain which ordered pairs, based on their signs: LENGTHS OF HORIZONTAL AND VERTICAL SEGMENTS Two points with the same y-coordinate lie on the same horizontal line, and two points with the same x-coordinate lie on the same vertical line. Find the distance between a horizontal or vertical segment by taking the absolute value of the difference of the two points. Example: Find the length of the line segment AB and the line segment BC. Points Sign of Coordinates Quadrant (2,3) (–2,3) (–3,–2) (3,–2) (+,+) (–,+) (–,–) (+,–) I II III IV II I III IV (−2,3) (2,3) (−3,−2) (3,−2) – THE GRE QUANTITATIVE SECTION– 200 . BC. Points Sign of Coordinates Quadrant (2, 3) ( 2, 3) (–3, 2) (3, 2) (+,+) (–,+) (–,–) (+,–) I II III IV II I III IV ( 2, 3) (2, 3) (−3, 2) (3, 2) – THE GRE QUANTITATIVE SECTION 20 0 . area of the cube = 16 ϫ 6 = 96. r h – THE GRE QUANTITATIVE SECTION 198 ■ To find the surface area of a right circular cylinder, use the formula A = 2 ␲ r 2 + 2 ␲ rh. CIRCUMFERENCE Circumference is the. use the formula A = bh. ■ To find the area of a rectangle, use the formula A = lw. ■ To find the area of a square, use the formula A = s 2 or A = ᎏ 1 2 ᎏ d 2 . w l h b r h b = Area – THE GRE QUANTITATIVE