Math, asked by ayushpandey66607874, 3 months ago


1. Two parallel sides of a trapezium ABCD are of lengths 10 cm and 19 cm respectively and the distance between them is 12 cm. find the area of the trapezium ​

Answers

Answered by Anonymous
4

A trapezium is a quadrilateral having one pair of parallel opposite sides. In the given figure, ABCD is a trapezium in which AB ∥ DC.

Area of a Trapezium:

Let ABCD be a trapezium in which AB ∥ DC, CE ⊥ AB, DF ⊥ AB and CE = DF = h.  

Prove that:

Area of a trapezium ABCD = {¹/₂ × (AB + DC) × h} square units.

Proof:     Area of a trapezium ABCD

           = area (∆DFA) + area (rectangle DFEC) + area (∆CEB)

           = (¹/₂ × AF × DF) + (FE × DF) + (¹/₂ × EB × CE)

          = (¹/₂ × AF × h) + (FE × h) + (¹/₂ × EB × h)

           = ¹/₂ × h × (AF + 2FE + EB)

           = ¹/₂ × h × (AF + FE + EB + FE)

           = ¹/₂ × h × (AB + FE)

           = ¹/₂ × h × (AB + DC) square units.

           = ¹/₂ × (sum of parallel sides) × (distance between them)

Formula of Area of a trapezium = ¹/₂ × (sum of parallel sides) × (distance between them)

Solved Examples of Area of a Trapezium

1. Two parallel sides of a trapezium are of lengths 27 cm and 19 cm respectively, and the distance between them is 14 cm. Find the area of the trapezium.

Solution:  

Area of the trapezium

     = ¹/₂ × (sum of parallel sides) × (distance between them)  

     = {¹/₂ × (27 + 19) × 14} cm²

     = 322 cm²

2. The area of a trapezium is 352 cm² and the distance between its parallel sides is 16 cm. If one of the parallel sides is of length 25 cm, find the length of the other.

Solution:  

Let the length of the required side be x cm.  

Then, area of the trapezium = {¹/₂ × (25 + x) × 16} cm²  

                                             = (200 + 8x) cm².  

But, the area of the trapezium = 352 cm² (given)

Step-by-step explanation:

Answered by Anonymous
0

Answer:

area of trapezium is 184cm^2.

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