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RealLife Math Phần 2

Tham khảo tài liệu 'reallife math phần 2', ngoại ngữ, anh ngữ phổ thông phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Area Areas of geometric shapes Geometric figure Dimensions Formula for area rectangle width W height H A WH square side length H A H2 circle radius R A R2 triangle base B height H A 1 2 BH parallelogram base B height H A BH trapezoid base B top T height H A 1 2 B T H Figure 1. standard formulas were worked out centuries ago for simple rounded objects like cones spheres and cylinders these formulas are listed in many math books. For example the area of a sphere of radius R is A 4 R2 tc pronounced pie is a special number approximately equal to 3.1416 see the article on Pi in this book . The Earth which is basically sphere-shaped has an average radius of 6 371 kilometers km or about 3 956 miles. Its surface area is therefore A 4 6 3712 510 060 000 km2 which is about 316 750 000 square miles. The Earth is 53 times the area of the United States. give correct units for length and area. However in mathematics it is common to not use units. The norm is to say that an imagined rectangle has a length of 4 a height of 5 and an area of 4 X 5 20. AREAS OF OTHER COMMON SHAPES The simplest rectangle is a square which is a rectangle whose four sides are all of equal length. If a square has sides of length H then its area is A H X H H2. The standard formulas for finding the areas of other simple geometric figures are depicted in Figure 1. Notice that in all the area formulas two measures of length are multiplied not added. This means that whenever an object is made larger its area increases faster than its height or width. For example a square that has sides of length 2 has area A 22 4 but a square that is twice as tall with sides of length 4 has area A 42 16 which is four times larger. Likewise making the square three times taller with sides of length 6 makes it area A 62 36 which is nine times larger. In general a square s area equals its height squared therefore its area increases in proportion to or goes as the square of the side length. Consequently a common rule of thumb for