Find area of trapezium whose parallel sides are 34 and 20 cm and two sides are 13cm and 15 CM
Answers
Given=A trapizium.
Prove that = its area
Construction = draw a line parallel to one side of non parallels side of trapizium.
We get there is two figures in trapizium that is a triangle $ parallogram .
Now first find triangle area by heron's formula .
In triangle sides is 15cm,13cm,14cm(14cm because in parallogram hram all sides are equal and in parallogram one is 20 so it's parallel is also 20 so 34-20=14)
Perimeter of triangle 15+13+14=42cm
Then find semi perimeter 42÷2=21cm
Area of triangle =root of 21(21-15)(21-13)(21-14)
=root of 21×6×8×7
= make its factor that is root of 3×7×3×2×2×2×2×7
Make pair that is 3×7×2×2=84cmsquare
Area of triangle = 84cmsquare
1/2×b×h=84
1/2×14×h=84
h=84÷7=12
H=12cm
In second figure parallogram
Area of parallogram =base×height
Base=20cm,height =12cm
A=20×12=240cm square
Area of trapizium =area of triangle +area of parallogram
Area of trapizium =84+240=324cm square