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The side of a square is 20 cmfind the areas of the circumscribed and inscribed circles?
The radius length r of the inscribed circle equals to one half of the length side of the square, 10 cm.
The area A of the inscribed circle: A = pir2 = 102pi ≈ 314 cm2
The radius length r of the circumscribed circle equals to one half of the length diagonal of the square.
Since the diagonals of the square are congruent and perpendicular to each other, and bisect the angles of the square, we have
sin 45⁰ = length of one half of the diagonal/length of the square side
sin 45⁰ = r/20 cm
r = (20 cm)(sin 45⁰)
The area A of the circumscribed circle: A = pir2 = [(20 cm)(sin 45⁰)]2pi ≈ 628 cm2.
What else can I help you with?
A square is inscribed in a circlethe diameter is congruent to?
the side of the square
How many circles can fit in an square?
Depends on the size of the circles and the square.
What is the definition of an inscribed square?
An inscribed square is a regular polygon with four sides such that each of its vertices is on the boundary of some other shape which lies wholly outside the square.
If you have a square inscribed in a circle what is the diameter of the circle congruent to?
The sides of the Square.
How much larger is the side of a square circumscribing a circle 155 cm indiameter than a square inscribed in the same circle?
The circumscribing square has sides of length 155 cm. The inscribed square has diagonals of 155 cm and so has sides of 155/sqrt(2) cm. The sides of a circumscribing square is always larger than those of the inscribed square by sqrt(2) = 1.4142 (approx). The area of a circumscribing square is always larger twice as large as that of the inscribed square.
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
What was the size of squares with concentric circles?
The size of squares with concentric circles typically refers to the dimensions of the square that contains the circles. Each circle is inscribed within the square, with its diameter equal to the length of the square's side. As more circles are added, each concentric circle has a progressively smaller diameter, centered within the square. The specific size of the square can vary based on the design or purpose of the arrangement.
Circumscribe in a sentence?
He circumscribed the square with a circle
What is the area of the region bounded by its inscribe and circumscribe circle whose side of a square is 10cm?
If I understand your question correctly, you would need to subtract the area of the inscribed circle from the circumscribed circle. Which would approximately be 78.60cm squared.
What is a cynosure of Pi?
A circle with a diameter of 2 is the guiding cynosure when Pi is the square of all possible circles: If the square root of Pi defines the side of a square and that square can be inscribed within a circle or enclose a circle, then the diameters of all possible circles between the largest and smallest include the circle of which Pi is its perfect square (a diameter of 2).
If four congruent circles are inscribed in a square with a side length of 20 mm as shown find the area of the shaded region?
It could mean: 202 -4*pi*52 = 86 square mm rounded to nearest integer
What has a square and 2 circles?
Two circles with a square on top
Can a circle be inscribed in a square?
Yes.
A square is inscribed in a circlethe diameter is congruent to?
the side of the square
How could you contrust a rhombus circumscribed in a circle?
You cannot circumscribe a "true rhombus". The opposite angles of a circumscribed quadrilateral must be supplementary whereas the opposite angles of a rhombus must be equal. That means a circumscribed rhombus is really a square.
How many circles can fit in an square?
Depends on the size of the circles and the square.
What is the definition of an inscribed square?
An inscribed square is a regular polygon with four sides such that each of its vertices is on the boundary of some other shape which lies wholly outside the square.
