a field is in the shape of trapezium those parallel sides are in 22m and 10m. And non parallel sides are 14m and 13m. find the area of the field.
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Answer:
of early knowledge and unnumbered kinds
Answer:
Given ABCD is a field. Draw CG ⊥ AB from C on AB, and CF parallel to DA.
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.
DC = AF = 10 m, DA = CF = 13 m (opposite sides of parallelogram)
So, FB = 25 - 10 = 15 m
In ∆CFB, a = 15 m, b = 14 m, c = 13 m.
Semi Perimeter(s) = (a + b + c)/2
s = (15 + 14 + 13)/2
s = 42/2
s = 21 m
By using Heron’s formula,
Area of ∆CFB = √s(s - a)(s - b)(s - c)
= √21(21 - 15)(21 - 14)(21 - 13)
= √21 × 6 × 7 × 8
= 84 m2
Also,
Area of ∆CFB = 1/2 × base × height
84 = 1/2 × BF × CG
84 = 1/2 × 15 × CG
CG = (84 × 2)/15
CG = 11.2 m
Area of trapezium ABCD = 1/2 × sum of parallel sides × distance between them
= 1/2 × (AB + DC) × CG
= 1/2 × (25 + 10) × 11.2
= 196 m2
Hence the area of the field is 196 m2.