Given Information:

• ABCD is a trapezium


• AB is parallel to DC


• AB = 78 cm


• CD = 52 cm


• AD = 28 cm


• BC = 30 cm

Formula:
The area of a trapezium can be calculated using the formula:
Area = (1/2) * (Sum of parallel sides) * (Distance between the parallel sides)

Step 1: Identify the Parallel Sides
From the given information, we can identify that AB and DC are the parallel sides of the trapezium.

Step 2: Calculate the Distance between the Parallel Sides
To calculate the distance between the parallel sides, we need to find the height of the trapezium. In this case, the height can be determined by the length AD.

Step 3: Calculate the Sum of Parallel Sides
The sum of the parallel sides can be calculated by adding the lengths of AB and DC.

Step 4: Calculate the Area
Using the formula for the area of a trapezium, we can substitute the values we have obtained in the previous steps to calculate the area.

Calculation:
Given:
AB = 78 cm
CD = 52 cm
AD = 28 cm
BC = 30 cm

Step 1: Identify the Parallel Sides
AB and DC are the parallel sides.

Step 2: Calculate the Distance between the Parallel Sides
The distance between the parallel sides is equal to the length of AD, which is 28 cm.

Step 3: Calculate the Sum of Parallel Sides
The sum of the parallel sides is equal to the sum of AB and DC, which is 78 cm + 52 cm = 130 cm.

Step 4: Calculate the Area
Using the formula for the area of a trapezium:
Area = (1/2) * (Sum of parallel sides) * (Distance between the parallel sides)
Area = (1/2) * 130 cm * 28 cm
Area = 1820 cm^2

Answer:
The area of the trapezium ABCD is 1820 cm^2.

65cm