Q. 144.4( 20 Votes )

# 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 :

**Given:** Parallel sides of trapezium = 25 m and 10 m

Non – parallel sides of trapezium = =14 m and 13 m

**To Find:** Area of the field

**Concept Used:**

If sides of a triangle are a, b, and c, then area of a triangle is given by:

Where s = semiperimeter of the triangle

**Diagram:**

**Construction:**

From C, draw CE || DA.

**Explanation:**

Now, we can see that ADCE is a parallelogram in which AE || CD and AD || CE.

Now, we can get,

AE = 10 m and CE = 13 m

BE = AB – AE [From the figure]

Therefore,

BE = 25 m – 10 m = 15 m

Now Area of trapezium = Area of Parallelogram AECD + Area of triangle ECB

Let us first calculate the area of a triangle,

s = 21 m

Area = 3 × 7 × 4 m^{2}

Area of Δ ECB = 84 m^{2}

We also know that Area of Δ ECB = 1/2 (BE × CL)

84 = 1/2 (15 × CL)

15 × CL = 168

CL

CL = Height of the parallelogram

Now, Area of parallelogram ADCE = Base × Height

Area of parallelogram = 112 m^{2}

**Hence, Area of Trapezium ABCD = (84 + 112) m ^{2} = 196 m^{2}.**

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