PLANE GEOMETRY

This chapter will discuss the forms fields in two-dimensional space, salesmen andextents of these fields, the form is a lot to do with economic activity (businessand management), especially regarding the extent of the field. Moreover introduced two magnitudesangles are degrees and radians and the relationship between the two units of this size.8.1 AngleSuppose we draw two straight lines AB and AC intersect at point A (seefigure 8.1), these two lines form an angle with vertex A and angle A is calleddenoted by: ÐBAC or can also be written as ÐCAB. Lines AB and ACcalled the foot of the angle BAC angle. To measure the amount of ÐBAC use rulescounter-clockwise with a right turn, then a positive value if the direction angleturn left and a negative value if the direction of turn the corner to the right, the angleexpressed in degrees. So great ÐBAC expressed by q 0Figure 8.1.1 Lines AB and AC lines forming ÐBACThere are several names angles formed by the angle, in Figure 8.1.1 ÐBACnamed because of the acute angle of less than 90o angle A, if the angle is 90oit is called a right angle, and if the angle of more than 90 ° is called an obtuse angle.UNIT LONG RELATIONSHIP WITH DEGREESTwo kinds of units are commonly used to determine the size of the angle is radians anddegrees. This section will discuss understanding the relationship between radians and degrees withradians. Draw a circle with center O and radius r as in Figure 8.1.2.Figure 8.1.2 Major Ð AOB = 1 radianSuppose AB an arc on the circle whose length is equal to the radius of the circle r.Great central angle AOB facing arc AB as one radian. Because mobilecircle equal to 2p r (p »3.14), this means that the central angle is: 2pradians. Large circle with one round corner is so 1o = 360o 360o1Unitthe smaller of the degrees are minutes and seconds, 10 = 60 'and 1' = 60 ". So:2p radians = radians = 360o or 180o 1p equation is the basic equation betweenradians and degrees, therefore:1 radian =180p »57 17 '45"1o =p180 »0.01745 radians8.2 FLAT FIELD TOURThe circumference of a flat wake up covered a number of long sides, can alsosaid that the circumference of a flat wake is the distance when a wakesurrounded reach back into place.SQUARE AND RECTANGLEBuild a rectangular flat is flat wake rectangle with cornerselbows at each corner, which has a length and width. While the squareare special circumstances of the rectangle that is the length and width are the same.As shown in Figure 8.8.2.4.Figure 8.8.2.4 Square and RectangleThe circumference of the rectangle is the distance around the sides if andreturn to starting point. For rectangles, rounds (K) is twice the length (p)plus two times the width (l) and expressed as:K = 2 p + 2l = 2 (p + l)For the square, because the lengths of the same sisiya (s) around the square then given by:K = 2s + 2s = 4sEXAMPLE 8.8.2.4Calculate the circumference of a rectangle with a length of 20 units wide and 15 units!AnswerRoving rectangle is:K = 2 (p + l) = 2 (20 +15) = 70 unitsEXAMPLE 8.2.2Calculate the circumference of a square with sides length of 20 units!AnswerRoving square are: K = 4s = 4'20 = 80 unitsParallelogram, kite - kite and trapeziumRectangular forms that are: Line parallelogram, kite and Trapezoid.Parallelogram has two pairs of sides are parallel, the two pairs of kitessides the same length while the trapezoid only has a pair of parallel sides. Formflat wake is shown in Figure 8.2.2Figure 8.2.2 Build flat Parallelogram, Kite and TrapezoidThe circumference of this rectangle awake by calculating the distance, if the orbitThis rectangular wake up and return to point of origin. Thus, for each roundBanun each rectangle is:* Line of parallelogram: K = 2 (p + l)* Kites: K = 2 (p + l)* Trapezoid: K = k + l + m + nTRIANGLEConsider Figure 8.2.3, shown in the picture that the rectangle drawn aline through one of the diagonals will be created in the form of planetriangle.Figure 8.2.3 TriangleRoving triangle expressed by adding three sides:1 2 3 K = S + S + SThere are 3 types of triangle are:* Triangle: one angle brackets* Isosceles triangle: two sides of the same length* An equilateral triangle: three sides equal in lengthCIRCLEObjects forms a circle often you come across in everyday life.Notice the wheels of the vehicle, round watches, medals, coinsare examples of objects that circle. The circle shape is obtainedby determining the domicile or the set of all points withinfixed to a point (Figure 8.2.4). Fixed point (xo, yo) is said to centercircle and the distance r is said to be the radius of the circle.Figure 8.2.4Circumference of a circle is equal to two times p times the radius, or write:K = 2p r8.3 BroadThe total area of ​​a flat wake, hereinafter referred to as broad is the size of theshows besarmya flat surface to seal the wake. Area of ​​a wakeflat expressed by L, which formulas broad flat wake that has beenwe learned we review again.SQUARE AND RECTANGLEBuild a rectangular flat is flat wake rectangle with cornerselbows at each corner, which has a length and width. While the squareare special circumstances of the rectangle that is the length and width are the same.As shown in Figure 8.1.2. The area of ​​a rectangle is the number of scalederivatives that can cover the surface of the rectangle. If the length of the squareunit length is p and the width of the rectangle is l units, then the area of ​​the squarelength are:L = p 'lWhile the area of ​​the square is the side (s) multiplied by the hand (s) and is given by:L = s' s = s 2EXAMPLE 8.3.1Find the area of ​​a square the Committee ng of length 8 cm and width 4 cmAnswerL = p 'l = 8cm '4 cm = 32 cm2EXAMPLE 8.3.2Find the area of ​​a square with a side length of 4 mAnswerL = s' = s = 16 m2 4m'4mTRIANGLEConsider Figure 8.3.1. Seen in the picture that the area of ​​the triangle ABC equal to ½ADCF plus a large rectangle area of ​​rectangle ½ DBFC the broad triangle ABCequal to the area of ​​a rectangle ½ ADCE and DBFC. So the area of ​​the triangle can beformulated as follows:Figure 8.3.1If the length of the base (AB) ABC is a triangle and the length of the line CD is high t,then the area of ​​triangle ABC can be written:EXAMPLE 8.3.3Find the area of ​​a triangle whose base is 8 cm long and 4 cm highAnswerParallelogramTo get a broad parallelogram consider Figure 8.3.2. Create a line of highpair of parallel sides, cut into triangles and stick to the right sideleft triangle, the shape into a square pedestal panjang.Misalkan long rangeknown a parallelogram and the height tFigure 8.3.2Jajaran parallelogram and rectangle formed fromTriangle piece lineup parallelogramSo vast jajajaran parallelogram is given by:L = a × tEXAMPLE 8.3.4Find the area of ​​a parallelogram whose base 8 cm long and 4 cm highAnswerL = a × t = 8cm × 4cm = 32 cm2