Question

The parallel sides of a trapezium are 52cm and 27cm and the other two sides are 25cm and 30 cm find the area of a trapezium

Answer 1

let ABCD is a trapezium having parallel sides are AB = 27cm , BC = 52 cm and non parallel sides are AB = 30 cm and CD = 25 cm

since , AB is parallel to BC . so then

AD = BE = 27 cm

and AB = DE = 30 cm

Find EC :
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EC = BC - BE = 52 - 27 = 25 cm

Find the are of ∆DEC:
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in ∆DEC ,

perimeter = 30 + 25 + 25 = 80 cm

semiperimeter s = 80 / 2 = 40 cm

by Heron's formula:
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area of ∆DEC

=√[s ( s - 30 ) ( s - 25 ) ( s - 25 )]

= √[40( 40 - 30) (40 - 25 ) (40 - 25 ) ]

= √(40 × 10 × 15 × 15 )

= √90000 = 300 cm^2 -----------(1)

again , from ∆DEC:
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area of ∆ DEC = (base × (height )/ 2

= ( 25 × h )/ 2 = 25h / 2 cm^2 ---(2)

Since , we know a triangle can not have different areas .

so then , equalize (1) and (2) and

solve for 'h' :
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300 = 25h / 2

25h = 600 => h = 24 cm

distance between the parallel sides :

h = 24cm

Find the area of trapezium:
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area of trapezium = 1 / 2 (sum of parallel sides) × distance between the parallel sides

= 1/ 2 ( AD + BC) × h

= ( 1/2 ) × ( 27 + 52 ) × 24

= 79 × 12 = 948 cm^2

Answer : area of trapezium = 948 cm^2