A field is in a shape of a trapezium whose parallel sides are 35m and 15m. The non parallel sides are 16 m and 18 m . Find the area of the field.
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Draw a line AE, which is parallel to BC
⇒ABCE is a parallelogram
⇒ Area of trapezium = Area ΔADE + Area ABCE
In ΔADE, as the lengths of the three sides are 13,14and15, we can use Heron's Formula to find its area.
Heron's formula : A=√s(s−a)(s−b)(s−c)
where s=perimeter2, and a,b,c are the three known sides.
⇒s=13+14+152=21
⇒ Area of ΔADE=√21(21−13)(21−14)(21−15)
=√(21⋅8⋅7⋅6)=√7056=84
84=12⋅15⋅h
⇒h=84⋅215=11.2
Area ABCE=10×h=10×11.2=112
Hence Area of trapezium ABCD= Area ΔADE + Area ABCE
=84+112=196 m2
⇒ABCE is a parallelogram
⇒ Area of trapezium = Area ΔADE + Area ABCE
In ΔADE, as the lengths of the three sides are 13,14and15, we can use Heron's Formula to find its area.
Heron's formula : A=√s(s−a)(s−b)(s−c)
where s=perimeter2, and a,b,c are the three known sides.
⇒s=13+14+152=21
⇒ Area of ΔADE=√21(21−13)(21−14)(21−15)
=√(21⋅8⋅7⋅6)=√7056=84
84=12⋅15⋅h
⇒h=84⋅215=11.2
Area ABCE=10×h=10×11.2=112
Hence Area of trapezium ABCD= Area ΔADE + Area ABCE
=84+112=196 m2
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