The feild is in the shape of trapezium whose parallel sides are 25m and 10m.The no n parallel sides are 14m and 13 m. Find the area of the feild
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8th
Maths
Understanding Quadrilaterals
Kinds of Quadrilateral
A field is in the shape of ...
MATHS
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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Let ABCD be a trapezium with,
AB∥CD
AB=25m
CD=10m
BC=14m
AD=13m
Draw CE∥DA. So, ADCE is a parallelogram with,
CD=AE=10m
CE=AD=13m
BE=AB−AE=25−10=15m
In ΔBCE, the semi perimeter will be,
s=
2
a+b+c
s=
2
14+13+15
s=21m
Area of ΔBCE,
A=
s(s−a)(s−b)(s−c)
=
21(21−14)(21−13)(21−15)
=
21(7)(8)(6)
=
7056
=84m
2
Also, area of ΔBCE is,
A=
2
1
×base×height
84=
2
1
×15×CL
15
84×2
=CL
CL=
5
56
m
Now, the area of trapezium is,
A=
2
1
(sumofparallelsides)(height)
A=
2
1
×(25+10)(
5
56
)
A=196m
2
Therefore, the area of the trapezium is 196m
2
.
solution