Area of Trapezium/Trapezoid

A trapezoid is a 4-sided flat shape with straight sides that has a pair of opposite sides parallel.  Before looking trapezoid area, should know its parts. See the information below :

• The bottom side (base b ) parallel to the top side (base a) .
• The distance from one base to the other called height (h).

In the plane shapes are often written in capital letters at the vertex. This is to facilitate naming. For example, the trapezoid KLMN. KL means the line from  K point to L point, LM means the line from L point to M point, MN means the line from point M point to N point, KN means the line from K point to the N points.


Area of ​​trapezoid can be determined using the formula of triangle area. You do this by dividing the trapezoid
into two triangles. Then the triangle area summed.

Area of ​​trapezoid ABCD can be found by adding up the area of ​​triangle BAD with area of ​​triangle BCD

• BAD = ½ x AB x AD

                   = ½ x 6 x 5

                   =  ½ x 30

                   = 15 area unit

• BCD =  ½ x CD x BE

                   =  ½  x 9 x 5

                   =  ½  x 45

                   = 22,5 area unit

• ABCD = 15 + 22, 5

                      = 37, 5 area unit


Surface area of ​​the trapezoid = Area of ​​triangle I (BAD) + Area of ​​triangle  II (BCD)
                                                    =  ½ x a x h + ½ x bx h
                                                    = ½ (a+b) x h 

From the trapezoid area formula can be find high and the length of the trapezoid base.

• height = 2A/a + b
• a  base = (2A/h) - b
• b  base = (2A/h) - a

Example : 
1.  A trapezoid has 10 cm and 14 cm bases, height = 7 cm. What is the area ?
     Area = ½  x ( a + b) x h
               = ½ (10+14) x 7
               = ½ (24 ) x 7
               = 12 x 7
               =  84 cm
2.  A trapezoid has 8 cm and 12 cm bases, area = 90 cm. What is the height ?
      height = 2A/a + b
                  = 2(90)/8+12
                  = 180/20
                  = 9 cm
3.  A trapezoid has b base 16 cm, 14 cm height and area = 252 cm. What is the a base ?
     a  base = (2A/t) - b
                  = (2 x 252/14) - 16
                  = (504/14) - 16
                  = 36 - 16
                  = 20 cm
4. A trapezoid has a base 14 cm, 12 cm height and area = 180 cm. What is the b base ?
     b  base = (2A/t) - a
                  = (2 x 180/12) - 14
                  = (360/12) - 14
                  = 30 - 14
                  = 16 cm

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