Area of Kite

You have to learn the triangle and the area of ​​the triangle. Isosceles triangles have special properties. Two isosceles triangles are the same length of its base can be compiled into a wake kites. Kites are rectangular. The kite has two pairs of sides of equal length. Kite is formed of two isosceles triangles. Both triangles have the same base length, but different height.  

Area of ​​kite can also be found using the formula area of ​​the triangle. By calculating the area of ​​the isosceles triangles that make up the kite. After that, the results are summed. Area of ​​kite ABCD can be found by summing the area ΔADC with ΔABC.

• Area  ΔADC =  ½ x  AC x OD

                                           = ½ x  8 x 4
                                           = 4 x 4
                                           = 16 area unit

• Area  ΔABC =  ½ x  AC x OB

                                           =  ½ x 8 x 9

                                           = 4 x 9

                                           = 36 area unit

• Area  ΔABC  = 16 + 36

                                = 52 area unit

Area ABCD = Area ΔADC + Area  ΔABC
                     = ½ x  AC x OD + ½ x  AC x OB
                            = ½ x AC ( OD + OB)
                            = ½ AC x BD 
                            = ½ x d1 x d2

 d1 and d2 is the diagonal of the kite. From the area of kite kite above, can be determined the diagonals.

• d1  = 2A/d2
• d2 = 2A/d1

Example :

1. A kite has d2 = 15 cm and area = 150 cm

     d1 = 2x150/15

           = 300/15

           = 20 cm

2.  A kite has d1 = 20 cm and area = 250 cm

      d2 = 2x 250/20

            = 500/20

            = 25 cm

3.  John want to make a kite. Two pieces of bamboo are made John with 48 cm and 44 cm 

      long.  If the kite has made, how area of the kite ?

      Area = ½ x d1 x d2

                 = ½ x 48 x 44

                 = 24 x 44

                 = 1.056 cm

4. On the wall there is a kite-shaped image. Area of the picture = 5.400 cm² and one of the 
    diagonal length is 120 cm. How long is the other diagonal ?
    d2 = 2A/d1
          = 2 x 5.400/120
          = 10.800/120
          = 90 cm

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Area of Triangle

Triangle is polygon ( a plane shape that have three or more straight sides) with three angles and three sides( One of the lines that make a flat (2-dimensional) shape. Or one of the surfaces that make a solid (3-dimensional) object). There are three special names given to triangles that tell how many sides (or angles) are equal. There can be 3, 2 or no equal sides/angles:

Various kinds of triangles according to angle.

• Acute triangle . The third large angle of less than 90 °.
• Right triangle. One large angle of 90 °.
• Obtuse triangle. Big one corner more than 90 ° and less than 180 °

Various kinds of triangles according to the side.

• Scalene triangle, three sides of unequal length.
• Isosceles triangle, two sides equal in length.
• Equilateral triangle, three sides equal in length.

Equilateral Triangle =    Three equal sides  Three equal angles, always 60°

Isosceles Triangle = Two equal sides   Two equal angles

Scalene  Triangle = No equal sides   No equal angles

The characteristics of the triangle

• Triangles have three sides.
• Vertex of the triangle there are 3
• The whole  angles of triangle is 180 °.

Area of triangle

Area = ½ x b x h ( b=base, h=height)

Example :
Base of triangle : 15 cm and height : 12 cm
Area = ½ × b × h
         = ½ × 15 × 12
         = 90 cm

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Area of Rhombus

A rhombus is a four-sided shape where all sides have equal length. Also opposite sides are parallel and opposite angles are equal. Another interesting thing is that the diagonals (dashed lines in second figure) of a rhombus bisect each other at right angles. Rhombus formed from an isosceles triangle and its shadow reflected on the base as the axis of symmetry. Isosceles triangle ABC is reflected to the side of the base AC, so it appears his shadow ACD. ACD is congruent with the ABC. 

The properties of a rhombus as follows :

1. The length of its four sides equal in length 

     and Opposite sides are parallel.

• AB = BC = CD = AD
• AB // DC dan AD // BC

2. Both rhombus diagonal bisect each other 

    the same length and intersect 

    perpendicularly.

3. Opposite angles equal.

• ∠BAD =  ∠BCD
• ∠ABC =  ∠ADC
• ∠BAE =  ∠DAE =  ∠BCE = ∠ DCE
• ∠ADE =  ∠CDE =  ∠ABE =  ∠CBE

4. Both diagonal are  axis of symmetry.

• Diagonal AC ┘└ BD
• Panjang AE = EC
• Panjang DE = EB

Area of Rhombus :

Area =  ½ x d1 x d2
Based on rhombus area can be found each diagonal.

• d1  = 2A/d2
• d2 = 2A/d1

Example :

1. A rhombus has diagonal 1 = 15 cm and diagonal 2 = 20 cm. What is the area ?

    Area = di x d2

             = 15 x 20

             = 300 cm

2. A rhombus has 300 cm area and one of the diagonal is 30 cm. What is the other diagonal ?

     d1 = 2A/d2

          = 2(300)/30

          = 600/30

          = 20 cm

3.  A rhombus has 187 cm area and one of the diagonal is 17 cm. What is the other diagonal ?

     d2 = 2A/d1

          = 2(187)/17

          = 374/17

          = 22 cm

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Area of Circle

The circle is a plane shape that the distance of every point on its side with the center of the circle is always the same.. The radius of the circle is the distance of the center to the edge of the circle. The radius is denoted by r. The circle has a center line. The center line twice the length of the radius. The center line is denoted by diameter (d). d = 2 × r. The Circumference is the distance around the edge of the circle. Pi (the symbol is the Greek letter π) is: The ratio of the Circumference  to the Diameter of a Circle.

• π = circumference/diameter = 3,1415926535897323846....
• A quick and easy approximation to π is 22/7 = 3,1428571...

A circle with a center point C has the following sections.

• C is the center of the circle.
• AC = CB = r = radius of the circle.
• AB = diameter of the circle
• AB = AC + CB = 2 × r = 2R = 2 × radius
• If the radius of a circle = r and diameter d = 2 × r or r =  ½ × d

Area of ​​a circle is  π  times the square of the radius of the circle Area =

Circle Area = π r2

When the area of ​​a circle is expressed by the diameter :
Area = πr2  → (note: r = ½  x d)
          = π (½ d) 2
         = π ( ¼ d)2 
          = ¼ π d2 

Circle Area = ¼ π d2

Diameter = 2 x radius

Circumference =2πr or πd

Example :
1.  A circle has 21 cm radius. What is area and circumference ?
     Area = π r 2 
               = 22/7 x 212
               = 1.386 cm
    Circumference = 2πr
                               = 2 x 22/7 x 21
                               = 44 x 21
                               = 132 cm

2.  A circle has 616 cm area and π = 22/7. What is r  ?

     Area    =  π  x r2

     616     = 22/7 x r2

    22 x r2 = 616 x 7

    22r2     = 4312
        r2      = 4312/22
        r2     = 196
        r       =  √196
        r       = 14 cm

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