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.

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Solution

Construction:
$\Rightarrow$ Draw $B E ∥ A D$ such that $D - E - C$
$\Rightarrow$ Draw $B M ⊥ D C$ such that $D - E - M - C$

$□ A B E D$ is parallelogram,
$\Rightarrow$ $A D = B E = 13 m$
$\Rightarrow$ $A B = D E = 10 m$
$\Rightarrow$ $B C = 14 m$
$\Rightarrow$ $D C = D E + E C$ .... $(∵ D - E - C)$
$∴ E C = 25 - 10$
$∴ E C = 15 m$

$\Rightarrow$ In $Δ B E C$
$\Rightarrow$ $2 S = 13 + 14 + 15$
$\Rightarrow S = 21 m$

$\Rightarrow$ Area of $△ B E C$

$\Rightarrow A = \sqrt{s (s - a) (s - b) (s - c)}$

$= \sqrt{21 (21 - 13) (21 - 14) (21 - 15)}$

$= \sqrt{21 \times 8 \times 7 \times 6}$

$= 84 m^{2}$

$\Rightarrow$ Area of $Δ B C E = \frac{1}{2} \times B M \times E C$

$\Rightarrow$ $B M = \frac{84 \times 2}{15}$

$= 11.2 c m$

$\Rightarrow$ Area of $□ A B E D = 11.2 \times 10 = 112 m^{2}$

$\Rightarrow$ Area of the field $□ A B C D$
$= 84 + 112 m^{2}$

$= 196 m^{2}$

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Question 9
A field is in the shape of a trapezium whose parallel sides are 25m and 10m.The non-parallel sides are14 m and 13 m. Find the area of the field.

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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.

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.