Find the area of a trapezium whose parallel sides are 25 cm and 13 cm and non parallel sides are 15 cm each. Find area of trapezium. It's urgent ...plzzzzzzz help...
Answers
Hope this helps.
See the picture
Given:- ABCD Is a trapezium
AB = 25 cm
DC = 13 cm
AD & BC = 15 cm
Construction:- Draw CE || AD
To Find :- Area of trapezium ABCD
Solution :- ADCE is a parallelogram ( AD || CE & AE || CD).
∴ AE = DC = 13 cm ( Opposite side of parallelogram are equal)
BE = AB - AE
BE = 25 - 13
BE = 12 cm
In ∆ BCE
S = a + b + c/2
S = 15 + 15 + 12 /2
S = 21
Area of ∆ BCE = √ s( s - a)(s - b)( s - c )
Area of ∆ BCE = √ 21(21-15)(21-15)(21-12)
Area of ∆ BCE = √ 21 × 6 × 6 × 9
Area of ∆ BCE = 18√21 cm^2 -----1
h is the height of ∆ BCE
Area of BCE = 1/2 ( Base × Height )
= 1/2(12)(h)
= 6h -----2
From 1 & 2
6h = 18√21
=> h = 3√21 cm
The height of trapezium ABCD is equal to height of ∆ BCE.
Area of trapezium = 1/2 ( AB + CD ) × h
= 1/2 (25 + 13) × 3√21cm^2
= 57√21 cm^2
