Hello MATE =_=

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Question:-

A field is in the shape of a trapezium whose parallel SIDES are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.

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 Solution:

Given: ABCD is a trapezium. Non-parallel sides are 14 m and 13 m. Parallel sides are 25 m and 10 m.

Construction: From point C draw CE∥DA completing parallelogram AECD. Also, draw CF⊥BE.

Now, we have AE=CD=10 m andAD=CE=14 m because AECD is a parallelogram.

So, BE=AB-AE=25-10=15 m

Semi-perimeter of  ∆BEC

= s

=(BE+CE+BC)/2

=(15+14+13)/2=42/2=21 m

Using Heron's FORMULA, 

Area of ∆BEC=

√{s(s−BE)(s−CE)(s−BC)}

=√{21(21−15)(21−14)(21−13)}

=√{21×6×7×8}

=84 m2         ........(1)

Area of ∆BEC=1/2× BE ×CF=84 m2

⇒CF=2×84/15=11.2 m

Area of parallelogram AECD 

=AE×CF=10×11.2=112 m2      ...... (2)

Adding (1) and (2), we get

Area of trapezium ABCD=Area of ∆BEC+Area of parallelogram AECD =84+112=196 m2

hope, this will help you.

Thank you______❤

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