A plot of land ABCD such that AB = 85m, BC = 75m, CD = 60m, DA = 50m and angle ACB =90 degrees . Determine the area of the plot in hectares correct to two decimal places

To determine the area of the plot, we need to follow these steps:

1. Calculate the area of the plot in square meters.
2. Convert the area from square meters to hectares.
3. Round the final result to two decimal places.

Step 1: Calculate the area of the plot in square meters.
To calculate the area of an irregular quadrilateral, we can break it down into two right-angled triangles and a rectangle.

In this case, we can consider triangle ABC and triangle CDA. Both triangles share side AC, which is common to both.

Area of triangle ABC = (1/2) * AB * BC
= (1/2) * 85m * 75m
= 3187.5 square meters

Area of triangle CDA = (1/2) * CD * DA
= (1/2) * 60m * 50m
= 1500 square meters

Now, we need to calculate the area of the rectangle CADB. The length of the rectangle is AC, and the width is BC.

Area of rectangle CADB = AC * BC
= 85m * 75m
= 6375 square meters

Total area of the plot = Area of triangle ABC + Area of triangle CDA + Area of rectangle CADB
= 3187.5 + 1500 + 6375
= 11062.5 square meters

Step 2: Convert the area from square meters to hectares.
1 hectare = 10,000 square meters

Area in hectares = (11062.5 square meters) / (10,000 square meters/hectare)
= 1.10625 hectares

Step 3: Round the final result to two decimal places.
The area of the plot, in hectares, correct to two decimal places, is approximately 1.11 hectares.