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F a polygon X is inscribed in an object Y then what can be said about each?
-- 'Y' is circumscribed about 'X' -- The area of 'X' is less than the area of 'Y'.
What is a true statement about a circle inscribed in a regular polygon?
The circle has a smaller area than the polygon.
What is the difference between inscribed and circumscribed in integration?
When rectangles are inscribed, they lie entirely inside the area you're calculating. They never cross over the curve that bounds the area. Circumscribed rectangles cross over the curve and lie partially outside of the area. Circumscribed rectangles always yield a larger area than inscribed rectangles.
What are the measures in a regular polygon?
The area of a regular polygon is given by the following formula: area =(1/2) (apothem)(perimeter).There are several other formulas that can be used. Regular Polygon Formulas are: N=number of sides, s= length, r = apothem (adiius of inscribed circle) R = radius of circumcircle. Using any of these formulas you can find the measurements of a regular polygon.
How can you find the area of a circle geometrically?
You can do an upper and lower bound by inscribing and circumscribing polygons. The more sides the polygon has, the more precise your answer will be. You inscribe a polygon by having the corners touch the circle's interior, and you circumscribe a polygon by having the midpoint of the sides touch the circle's exterior. Note that the polygon must by equilateral and equiangular for this method to be reasonably simple. Then simply find the area of the inscribed polygon - you know the circle is bigger than it, because the circle contains the polygon and has more space as well. Thus that number is your lower bound. Then find the area of the circumscribed polygon- same logic for the polygon being bigger than the circle. Area of circumscribed is your upper bound. Then typically average your upper and lower bound to get a reasonable estimate of the area of the circle. Of course, solving the problem algebraically is both simpler and more precise, but since you wanted a geometric answer, you got one.
F a polygon X is inscribed in an object Y then what can be said about each?
-- 'Y' is circumscribed about 'X' -- The area of 'X' is less than the area of 'Y'.
What is a true statement about a circle inscribed in a regular polygon?
The circle has a smaller area than the polygon.
What is the difference between inscribed and circumscribed in integration?
When rectangles are inscribed, they lie entirely inside the area you're calculating. They never cross over the curve that bounds the area. Circumscribed rectangles cross over the curve and lie partially outside of the area. Circumscribed rectangles always yield a larger area than inscribed rectangles.
What are the measures in a regular polygon?
The area of a regular polygon is given by the following formula: area =(1/2) (apothem)(perimeter).There are several other formulas that can be used. Regular Polygon Formulas are: N=number of sides, s= length, r = apothem (adiius of inscribed circle) R = radius of circumcircle. Using any of these formulas you can find the measurements of a regular polygon.
What is the ratio of the area of the circumscribed square to the area of the inscribed square?
If we denote the measure of the length side of the circumscribed square with a, then the vertexes of the inscribed square will point at the midpoint of the side, a, of the circumscribed square.The area of the circumscribed square is a^2The square measure of the length of the inscribed square, which is also the area of this square, will be equal to [(a/2)^2 + (a/2)^2]. Let's find it:[(a/2)^2 + (a/2)^2]= (a^2/4 + a^2/4)= 2(a^2)/4= a^2/2Thus their ratio is:a^2/(a^2/2)=[(a^2)(2)]/a^2 Simplify;= 2
How can you find the area of a circle geometrically?
You can do an upper and lower bound by inscribing and circumscribing polygons. The more sides the polygon has, the more precise your answer will be. You inscribe a polygon by having the corners touch the circle's interior, and you circumscribe a polygon by having the midpoint of the sides touch the circle's exterior. Note that the polygon must by equilateral and equiangular for this method to be reasonably simple. Then simply find the area of the inscribed polygon - you know the circle is bigger than it, because the circle contains the polygon and has more space as well. Thus that number is your lower bound. Then find the area of the circumscribed polygon- same logic for the polygon being bigger than the circle. Area of circumscribed is your upper bound. Then typically average your upper and lower bound to get a reasonable estimate of the area of the circle. Of course, solving the problem algebraically is both simpler and more precise, but since you wanted a geometric answer, you got one.
How did Archimedes estimate pi?
The approximate area of the circle lies between the areas of the circumscribed and the inscribed hexagons.
How is the formula of a polygon closely related to the formula of the area of a circle?
The area of a polygon is greater than the area of the largest circle that can be inscribed within the polygon and smaller that the area of the smallest circle in which the polygon can be enclosed. So the areas of two circles establish a lower and upper bound to the area of the polygon. In a similar fashion, the perimeter of the polygon are also bounded by the circumferences of the two circles. This also works in reverse. That is, the area of a circle lies between the area of an inscribed polygon and that of a polygon containing the circle. And, again, the same applies to the circumference/perimeter. In fact these bounds were used to calculate the value of pi.
What is the formula for finding the area of a regular polygon with perimeter P and apothegm length a?
Area of regular polygon: 0.5*apothem*perimeter
What are faces of a congruent regular polygon?
A regular polygon has equal sides and angles. A polygon has a surface area but a polyhedron has many faces as for example a pyramid.
If the midpoint of successive sides of a regular polygon are joined a smaller regular polygon is formed Find a polygon of such number of sides so that the area is half that of the larger?
The polygon is a Quadrilateral.
What is the area of a regular polygon if the radius is 8 cm?
The area of a regular polygon with n sides is the half of the product of its perimeter and the apothem. So that you do not have enough information to find the area of the polygon (for example how many sides it has, or the side length).
