What is the area of a section bounded by a closed elliptical figure whose major and minor segments measure 60 m and 40 m, respectively?
no solid mensuration here. Just regular plane geometry.
The area of an ellipse with semi-axes a and b is πab.
Note that if a=b, we have a circle of radius a, and area πa^2
a is 60m while b is 40m. then divide both 60m and 40m in to two so 60/2 and 40/2 the area is (pie)(30)(20) so the area is 1884.96m^2
To find the area of a closed elliptical figure, you can use the formula for the area of an ellipse:
Area = π * a * b
where "a" is the length of the semi-major axis and "b" is the length of the semi-minor axis.
In this case, the major and minor segments of the ellipse measure 60 m and 40 m respectively.
Thus, the semi-major axis (a) is half of the major segment, so a = 60/2 = 30 m.
Similarly, the semi-minor axis (b) is half of the minor segment, so b = 40/2 = 20 m.
Now, we can substitute these values into the formula to find the area:
Area = π * a * b
= π * 30 m * 20 m
= π * 600 m^2
So, the area of the section bounded by the closed elliptical figure is 600π square meters, or approximately 1884.96 square meters.
To find the area of a section bounded by a closed elliptical figure, you can use the formula for the area of an ellipse. The formula is given as A = π * a * b, where "a" and "b" represent the lengths of the major and minor axes, respectively.
In this case, the major axis measures 60 m and the minor axis measures 40 m.
So, to find the area, simply substitute the given values into the formula:
A = π * 60 * 40
Now, multiply 60 by 40:
A = π * 2400
To get a numerical approximation, you can multiply π by 2400. Using the approximation π ≈ 3.14159, the calculation is as follows:
A ≈ 3.14159 * 2400
A ≈ 7539.8216 square meters
Therefore, the area of the section bounded by the closed elliptical figure is approximately 7539.8216 square meters.