what is the area of a parabola inscribed in a rectangle 30cm long and 22cm wide
For an ellipse in the form
x^2/a^2 + y^2/b^2 = 1
the area of an ellipse us abπ
in your case a=15, b=11
area = 165π
I misread your question
The area of a parabola is (2/3)bh,
where b is the base and h is height
so in your case
Area = (2/3)(30)(22) = 440
To find the area of a parabola inscribed in a rectangle, we first need to understand what it means for a parabola to be inscribed in a rectangle. In this case, it implies that the vertex of the parabola lies on the midpoint of the rectangle's longer side.
To calculate the area of the parabola, we need to determine its height and base. The height will be the distance from the vertex to the upper side of the rectangle. The base will be the length of the rectangle.
Let's start by finding the base, which is already given as 30 cm.
Next, we determine the height by considering that the vertex lies on the midpoint of the longer side of the rectangle, which is 22 cm. Therefore, the height is half of this distance, which is 11 cm.
Now, we have the base and height of a rectangle that represents the parabola. To find the area of the rectangle, we multiply the base by the height:
Area = Base * Height
Area = 30 cm * 11 cm
Area = 330 cm^2
Thus, the area of the parabola inscribed in the given rectangle is 330 cm^2.