A piece of land in the shape of a trapezium is drawn on a map using the scale 1:500. The parallel sides are 5 cm and 2 cm, while the perpendicular distance between parallel sides is 4 cm. what is the actual area of the plot in square meter?
35m^2
First, we need to convert the area from cm^2 to m^2.
1 cm^2 = (1/100)^2 m^2
1 cm^2 = 0.0001 m^2
So, the area of the plot in m^2 would be:
A = 14 * 500^2 * 0.0001 m^2
A = 3.5 m^2
Therefore, the actual area of the plot is 3.5 square meters.
To find the actual area of the plot in square meters, we need to scale the measurements provided on the map to their actual size.
First, let's determine the lengths of the parallel sides in meters. Since the scale is 1:500, we need to convert the lengths from centimeters to meters.
Length of longer parallel side:
5 cm = 5 cm * (1 m / 100 cm) = 0.05 m
Length of shorter parallel side:
2 cm = 2 cm * (1 m / 100 cm) = 0.02 m
Next, we need to calculate the perpendicular distance between the parallel sides, also known as the height of the trapezium, in meters.
Height of the trapezium:
4 cm = 4 cm * (1 m / 100 cm) = 0.04 m
Now, we can calculate the area of the trapezium using the formula:
Area = (a + b) * h / 2
where a and b are the lengths of the parallel sides, and h is the height.
Area = (0.05 m + 0.02 m) * 0.04 m / 2
Area = 0.07 m * 0.04 m / 2
Area = 0.0028 m²
Therefore, the actual area of the plot is 0.0028 square meters.
the map figure has area
a = (5+2)/2 * 4 = 14 cm^2
The area is 14 * 500^2 cm^2
Now just convert that to m^2