Area of Trapezium



Here we will learn how to use the formula to find the area of trapezium.



Area of trapezium ABCD = Area of ∆ ABD + Area of ∆ CBD
= 1/2 × a × h + 1/2 × b × h
= 1/2 × h × (a + b)
= 1/2 (sum of parallel sides) × (perpendicular distance between them)

Area of trapezium




Worked-out examples on area of trapezium

1. The length of the parallel sides of a trapezium are in the rat: 3 : 2 and the distance between them is 10 cm. If the area of trapezium is 325 cm2, find the length of the parallel sides.

Solution:

Let the common ration be x,
Then the two parallel sides are 3x, 2x
Distance between them = 10 cm
Area of trapezium = 325 cm2
Area of trapezium = 1/2 (p1 + p2) h
325 = 1/2 (3x + 2x) 10
⇒ 325 = 5x × 5
⇒ 325 = 25x
⇒ x = 325/25
Therefore, 3x = 3 × 13 = 39 and 2x = 2 × 13 = 26

Therefore, the length of parallel sides area are 26 cm and 39 cm.


2. ABCD is a trapezium in which AB ∥ CD, AD ⊥ DC, AB = 20 cm, BC = 13 cm and DC = 25 cm. Find the area of the trapezium.

find the area of trapezium



Solution:

From B draw BP perpendicular DC
Therefore, AB = DP = 20 cm
So, PC = DC - DP
= (25 - 20) cm
= 5 cm

Now, area of trapezium ABCD = Area of rectangle ABPD + Area of △ BPC
△BPC is right angled at ∠BPC
Therefore, using Pythagoras theorem,
BC2 = BP2 + PC2
132 = BP2 + 52
⇒ 169 = BP2 + 25
⇒ 169 - 25 = BP2
⇒ 144 = BP2
⇒ BP = 12

Now, area of trapezium ABCD = Area of rectangle ABPD + Area of ∆BPC
                    = AB × BP + 1/2 × PC × BP
                    = 20 × 12 + 1/2 × 5 × 12
                    = 240 + 30
                    = 270 cm2



3. Find the area of a trapezium whose parallel sides are AB = 12 cm, CD = 36 cm and the non-parallel sides are BC = 15 cm and AG = 15 cm.

examples on area of trapezium



Solution:

In trapezium ABCD,
draw CE ∥ DA.
Now CE = 15 cm
Since, DC = 12 cm so, AE = 12 cm
Also, EB = AB - AE = 36 - 12 = 24 cm
Now, in ∆ EBC
S = (15 + 15 + 24)/2
= 54/2
= 27
= √(27 × 12 × 12 × 3)
= √(3 × 3 × 3 × 3 × 2 × 2 × 2 × 2 × 3 × 3)
= 3 × 3 × 3 × 2 × 2
= 108 cm2
Draw CP ⊥ EB.
Area of ∆EBC = 1/2 × EB × CP
108 = 1/2 × 24 × CP
108/12 = CP
⇒ CP = 9 cmTherefore, h = 9 cm

Now, area of triangle = √(s(s - a) (s - b) (s - c))
= √(27 (27 - 15) (27 - 15 ) (27 - 24))

Now, area of trapezium = 1/2(p1 + p2) × h
= 1/2 × 48 × 9
= 216 cm2


4. The area of a trapezium is 165 cm2 and its height is 10 cm. If one of the parallel sides is double of the other, find the two parallel sides.

Solution:

Let one side of trapezium is x, then other side parallel to it = 2x
Area of trapezium = 165 cm2
Height of trapezium = 10 cm
Now, area of trapezium = 1/2 (p1 + p2) × h
⇒ 165 = 1/2(x1 + 2x) × 10
⇒ 165 = 3x × 5
⇒ 165 = 15x
⇒ x = 165/15
⇒ x = 11
Therefore, 2x = 2 × 11 = 22
Therefore, the two parallel sides are of length 11 cm and 22 cm.

These are the above examples explained step by step to calculate the area of trapezium.



Mensuration

  • Area and Perimeter
  • Perimeter and Area of Rectangle
  • Perimeter and Area of Square
  • Area of the Path
  • Area and Perimeter of the Triangle
  • Area and Perimeter of the Parallelogram
  • Area and Perimeter of Rhombus
  • Area of Trapezium
  • Circumference and Area of Circle
  • Units of Area Conversion
  • Practice Test on Area and Perimeter of Rectangle
  • Practice Test on Area and Perimeter of Square

  • Mensuration - Worksheets
  • Worksheet on Area and Perimeter of Rectangles
  • Worksheet on Area and Perimeter of Squares
  • Worksheet on Area of the Path
  • Worksheet on Circumference and Area of Circle
  • Worksheet on Area and Perimeter of Triangle




  • 7th Grade Math Problems

    8th Grade Math Practice

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