question_answer

Length of the fence of a trapezium shaped field ABCD in 120 m. If BC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. Side AB is perpendicular to the parallel sides AD and BC.

Answer:

Sides of a trapezium are BC = 48 m, CD = 17 m and AD = 40 m, AB =?

Length of the fence of a trapezium shaped = 120 m

Perimeter of trapezium

= Length of fence of trapezium ABCD shaped

\[AB\text{ }+\text{ }BC\text{ }+\text{ }CD\text{ }+\text{ }AD\text{ }=\text{ }120\]

\[AB\text{ }+\text{ }48\text{ }+\text{ }17\text{ }+\text{ }40\text{ }=\text{ }120\]

\[AB\text{ }+\text{ }105\text{ }=\text{ }120\]

\[AB\text{ }=\text{ }120\text{ }\text{ }105\]

\[AB\text{ }=\text{ }15\text{ }m.\]

Two parallel sides of trapezium,

AD = 40 m, BC = 48 m.

Perpendicular height between them,

AB = 15 m

Then, the area of trapezium field

\[=\frac{1}{2}\times h\times \] (sum of parallel sides)

\[=\frac{1}{2}\times 15\times (40+48)\]

\[=\frac{1}{2}\times 15\times 88\]

\[=\text{ }660\text{ }{{m}^{2.}}\]