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Given that we have a trapezium and we need to find the perimeter and area of that trapezium.

Let us start solving by drawing a line parallel to side AC from point D. We get the figure as shown below:

We know that that the perimeter of a figure is equal to the sum of the length of all of its sides.

Perimeter of trapezium ABCD = 2.5dm + 5dm + 4dm +3dm.

Perimeter of trapezium ABCD = 14.5dm ---(1).

From the figure, we can see that the area of trapezium ABCD = area of Rectangle AEDC + area of triangle DEB ---(2).

We know that area of the rectangle with length ‘l’ and breadth ‘w’ is defined as $A=l\times w$.

Area of the Rectangle AEDC = $4dm\times 2.5dm$.

Area of the Rectangle AEDC = $10d{{m}^{2}}$ ---(3).

We know that area of the triangle with base ‘b’ and height ‘h’ is $A=\dfrac{1}{2}\times b\times h$. Here base length of the triangle DEB is 1dm and height of the triangle is 2.5dm.

Area of the Triangle DEB = $\dfrac{1}{2}\times 1\times 2.5$.

Area of the Triangle DEB = $1.25d{{m}^{2}}$ ---(4).

Substitute equation (3), (4) in equation (1).

Area of trapezium ABCD = 10 + 1.25.

Area of trapezium ABCD = $11.25d{{m}^{2}}$.