Question

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.​

Answer 1

Answer:

196m2

Step-by-step explanation:

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 = [latex]\frac { 1 }{ 2 }[/latex] x base x height

∴ [latex]\frac { 1 }{ 2 }[/latex] x 15 x h = 84

⇒ (10 + [latex]\frac { 82\times 2 }{ 15 }[/latex] = [latex]\frac { 56 }{ 5 }[/latex]

Now, area of a parallelogram = base x height

= (10 x [latex]\frac { 56 }{ 5 }[/latex]) = (2 x 56) m2 = 112 m2

So, area of the field

= area of ∆BCE + area of parallelogram ABED

= 84 m2 + 112 m2 = 196 m2