The length of a fence of a trapezium ABCD is 130m side ab is perpendicular to each of the parallel side AD &BC.if BC =54cm,AD=19cm,&AD=42cm,find the are of the field

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To find the area of the field, we need to know the height of the trapezium. However, it is not mentioned in the given information.

To solve this problem, we can use the Pythagorean theorem and other properties of a trapezium.

Let's assume that the height of the trapezium is 'h'.

According to the given information, side AB is perpendicular to both side AD and side BC. This means that AB is the altitude of the trapezium.

Using the Pythagorean theorem, we can find the length of the altitude AB:

AB² = AD² - BD²
AB² = 42² - (BC - AD)²
AB² = 42² - (54 - 19)²
AB² = 42² - 35²
AB² = 1764 - 1225
AB² = 539
AB = √539

Now we have the length of the altitude AB, which is the height of the trapezium.

To find the area of the field, we can use the formula for the area of a trapezium:

Area = (AB + CD) * h / 2

We have the values of AB (which is √539) and the lengths of AD and BC.

Area = (√539 + AD + BC) * h / 2

Substituting the given values:

Area = (√539 + 42 + 54) * h / 2
Area = (√539 + 96) * h / 2

Now, without knowing the value of the height 'h', we cannot calculate the exact area of the field.

To find the area, you need the height of the trapezium, which is not provided in the given information.