A piece of land in the shape of a trapezium is drawn on a map using the scale 1:500.The parallel sides are 5cm and 2cm , while the perpendicular distance between parallel sides is 4cm.what is the actual area of the plot in m2
To find the actual area of the plot in m², we need to first find the corresponding dimensions of the trapezium in real life.
Let's start by using the given dimensions in the map:
- The parallel sides measure 5cm and 2cm, respectively. These correspond to actual lengths of (5cm x 1/500) = 0.01m and (2cm x 1/500) = 0.004m.
- The perpendicular distance between the parallel sides measures 4cm. This corresponds to an actual height of (4cm x 1/500) = 0.008m.
Now we can use the formula for the area of a trapezium:
Area = (a + b)/2 x h
where a and b are the parallel sides and h is the height.
Substituting the actual dimensions, we get:
Area = (0.01m + 0.004m)/2 x 0.008m
Area = 0.00006 m²
Therefore, the actual area of the plot is 0.00006 m².
AAAaannndd the bot gets it wrong yet again!
the drawing has to be multiplied by 500, so its dimensions of
5cm, 2cm, 4cm represent actual dimensions of
25m, 10m, 20m
so the actual area is
(25+10)/2 * 20 = 350 m^2
I apologize for the mistake in my previous response. You are correct that the dimensions on the map need to be multiplied by 500 to obtain the actual dimensions of the trapezium in meters.
Using that conversion, we get:
- The parallel sides measure 25m and 10m, respectively.
- The perpendicular distance between the parallel sides measures 20m.
Using the formula for the area of a trapezium:
Area = (a + b)/2 x h
where a and b are the parallel sides and h is the height.
Substituting the actual dimensions, we get:
Area = (25m + 10m)/2 x 20m
Area = 350 m²
Therefore, the actual area of the plot is 350 m².
To find the actual area of the plot in square meters, we need to first calculate the area of the trapezium on the map and then scale it up to the actual size.
1. Calculate the area of the trapezium on the map:
Area map = (1/2) * (a + b) * h
where,
a = length of one of the parallel sides = 5 cm
b = length of the other parallel side = 2 cm
h = perpendicular distance between the parallel sides = 4 cm
Area map = (1/2) * (5 cm + 2 cm) * 4 cm
= (1/2) * 7 cm * 4 cm
= 14 cm^2
2. Convert the area from square centimeters to square meters using the scale of 1:500:
1 cm on the map represents 500 cm in real life, or 5 meters (since 1 meter = 100 cm).
Area actual = Area map * (1/500)^2
= 14 cm^2 * (1/500)^2
= 14 cm^2 * (1/250000)
= 0.000056 m^2
Therefore, the actual area of the plot is 0.000056 square meters.