A farmer has a field in the shape of the trapezium whose parallel sides are 10 km and 25km while the other side are 13km and 14km he grows paddy and wheat an equal amount find the yield of each crop
I have no idea what the yield is, but I can get the area.
Mark off the rectangle with the short base as one side. That leaves two right triangles, each with height h, and bases x and 15-x. So,
x^2 + h^2 = 14^2
(15-x)^2 + h^2 = 13^2
Solving that, we get h = 56/5
So, the area of the whole trapezoid is (10+25)/2 * 56/5 = 196
That means that each crop covers 98 km^2
To find the yield of each crop, we first need to calculate the area of the trapezium field.
The formula to calculate the area of a trapezium is:
Area = (1/2) * (a + b) * h
where a and b are the parallel sides, and h is the perpendicular height.
In this case, the parallel sides are 10 km and 25 km, and the other two sides are 13 km and 14 km. Let's calculate the perpendicular height first.
To find the perpendicular height, we can use the formula:
h = √(c^2 - ((d-b)/2)^2)
where c is the difference between the lengths of the parallel sides, and d and b are the lengths of the other two sides.
In this case, c = |10 km - 25 km| = 15 km, d = 13 km, and b = 14 km.
Plugging these values into the formula, we get:
h = √(15^2 - ((13-14)/2)^2)
h = √(225 - (1/2)^2)
h = √(225 - 1)
h = √224
h ≈ 14.97 km
Now that we have the height, we can calculate the area of the trapezium.
Area = (1/2) * (10 km + 25 km) * 14.97 km
Area = (1/2) * 35 km * 14.97 km
Area ≈ 523.95 km^2
Since the area of the field is the same for both crops, we can divide this area equally for both paddy and wheat.
Yield of paddy = Area / 2 = 523.95 km^2 / 2 ≈ 261.98 km^2
Yield of wheat = Area / 2 = 523.95 km^2 / 2 ≈ 261.98 km^2
Therefore, the yield of each crop is approximately 261.98 km^2.
To find the yield of each crop, we need to calculate the area of the trapezium field. The formula to find the area of a trapezium is:
Area = (a + b) * h / 2
where 'a' and 'b' are the lengths of the parallel sides and 'h' is the height or the perpendicular distance between the parallel sides.
In this case, the parallel sides of the trapezium are 10 km and 25 km, and the other two sides are 13 km and 14 km. To find the height, we can use the formula for the area of a triangle:
Area of a triangle = base * height / 2
We can find the height by considering one of the sides as the base and solving for the height:
For the side 13 km:
Area = 13 * h / 2
h = 2 * Area / 13
For the side 14 km:
Area = 14 * h / 2
h = 2 * Area / 14
Now, we can substitute the values of h in the formula for the area of a trapezium to find the total area of the field:
Area = (10 + 25) * (2 * Area / 13 + 2 * Area / 14) / 2
Simplifying this equation would yield the value of Area. Let's denote the yield of paddy as 'x' and the yield of wheat as 'y'. Since the farmer grows paddy and wheat in equal amounts, we can say that the area of paddy crops is 'x' and the area of wheat crops is 'y'.
Considering that the total area is equal to the sum of the areas of paddy and wheat crops, we can write:
Area = x + y
Therefore, by solving the equation for Area, we can get the value of x and y, which represents the yield of each crop.