4. 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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4. 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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Refer the given pic for the figure.
Construction:
Draw BE∥AD , Draw BM⊥DC
□ABED is parallelogram where:
AD = BE = 13 m
AB = DE = 10 m
BC = 14 m
=> DC = DE + EC .as D−E−C
∴EC = 25 − 10
∴EC = 15 m
Now, Using heron's formula,
In ΔBEC,
2s = 13+14+15
s = 21 m
Area of ∆BEC:
A = √[s (s−a)(s−b)(s−c)]
= √[21(21−13)(21−14)(21−15)]
=21 × 8 × 7 × 6
=84 m²
Area of ΔBEC = 84m²
Area of ∆ BCE = 1/2 × BM × EC
BM = 84 × 2/15
BM = 11.2 metres
Now, Area of □ABED = 11.2 × 10
= 112 m²
Area of □ABCD = Area of ∆BEC + Area of □ABED
= 84 + 112
= 196 m²
Area of field = 196 m².
Area of field = 196 m². _____________________________