a field is in the shape of a trapezium whose parallel sides are 25 m and 10 m and the non parallel sides are 14 m and 13m. find the area of the field
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Answer:
Step-by-step explanation:
- 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= 14+13+15 / 2
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
- Also, area of ΔBCE is,
A = 1/2 x Base x Height
84 = 1/2 x 15 x CL
84/2 x 15 = CL
CL = 56/5 m
- Now, the area of trapezium is,
A = 1/2 (sum of parallel sides)(height)
A = 1/2 (25 + 10) (56/5)
A = 196m 2
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