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. -Maths 9th

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. -Maths 9th
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Let the given field is in the form of a trapezium ABCD such that parallel sides are AB = 10 m and DC = 25 m Non-parallel sides are AD = 13 m and BC = 14 m. We draw BE || AD, such that BE = 13 m. The given field is divided into two shapes (i) ∆BCE, (ii) parallelogram ABED For ∆BCE: Sides of the triangle are a = 13 m, b = 14 m, c = 15 m (ii) For parallelogram ABED: Let the height of the ∆BCE corresponding to the side EC be h m. Area of a triangle = 12 x base x height ∴ 12 x 15 x h = 84 ⇒ (10 + 82×215 = 565 Now, area of a parallelogram = base x height = (10 x 565) = (2 x 56) m2 = 112 m2 So, area of the field = area of ∆BCE + area of parallelogram ABED = 84 m2 + 112 m2 = 196 m2
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