0
What is the ratio of the areas of a circle and a square if their perimeters are the same?
x = length of one side of square and r = radius of the circle therefore 4x = 2r * Pi therefore the radius of the circle is 2x/Pi therefore in terms of area x * x = Pi * ( 2x/Pi) * (2x/Pi) which gives a ratio of 1 : 4/Pi square area to circle area or 1 : Pi/4 circle to square x = length of one side of square and r = radius of the circle therefore 4x = 2r * Pi therefore the radius of the circle is 2x/Pi therefore in terms of area x * x = Pi * ( 2x/Pi) * (2x/Pi) which gives a ratio of 1 : 4/Pi square area to circle area or 1 : Pi/4 circle to square
No, not as a universal rule. To illustrate, think of a piece of string that is 12 feet long. That piece of string can go around the perimeter of a square that is 3 feet on each side (i.e. adding up the 4 sides, each 3 feet long, would yield a square that has a 12 foot perimeter). The area of that same square would be calculated as 3 times 3 which equals 9 square feet. Now picture that same string going around a rectangle that is 2 feet wide by 4 feet long. This is thus a shape that also happens to have a 12 foot perimeter. But the area for this shape would be 2 times 4 which equals 8 square feet. Thus two different shapes with identical perimeters do not have to have the same area. This simple illustration with two common shapes (a square and a rectangle) that have identical perimeters but different areas can be extended to the odd shapes. Having the same perimeter does not lead to the conclusion that the shapes then have the same area. Hope this helps, I had to think about it myself!
What else can I help you with?
What is the ratio of the areas of an equilateral triangle and a circle if their perimeters are same?
It is 0.6046 : 1 (approx).
Two triangles are similar and have a ratio of similarity of 3 1 What is the ratio of their perimeters and the ratio of their areas?
The ratio of their perimeters will be 3:1, while the ratio of their areas will be 9:1 (i.e. 32:1)
What is the width of two similar rectangles are 45 yd and 35 yd what is the ratio of the perimeters of the areas?
The ratio of their perimeters is also 45/35 = 9/7. The ratio of their areas is (9/7)2 = 81/63
If the ratio of the side lengths of two similar polygons is 31 what is the ratio of the perimeters?
Their perimeters are in the same ratio.
What is the ratio of the area of a circle to the area of a square when one side of the square is the radius of the circle?
Let's call the number 'K' ... the side of the square and the radius of the circle.-- the area of the square is [ K2 ]-- the area of the circle is [ (pi) K2 ]-- The ratio of the circle to the square is [(pi) K2 / K2 ] = pi
What is the ratio of the areas of an equilateral triangle and a circle if their perimeters are same?
It is 0.6046 : 1 (approx).
Two triangles are similar and have a ratio of similarity of 3 1 What is the ratio of their perimeters and the ratio of their areas?
The ratio of their perimeters will be 3:1, while the ratio of their areas will be 9:1 (i.e. 32:1)
What is the ratio of the area of a circle to the area of a square?
Circle and square are two entirely different shapes. But the ratio of areas of square to circle if their perimeter is equal is pi/4.
An equilateral triangle and a square have equal perimeters what is the ratio of the area of the triangle to the area of the square?
If an equilateral triangle and a square have equal perimeters, then the ratio of the area of the triangle to the area of the square is 1:3.
What are two different size squares that the ratio of their perimeters is the same as the ratio of their areas?
Assume square A with side a; square B with side b. Perimeter of A is 4a; area of A is a2. Perimeter of B is 4b; area of B is b2. Given the ratio of the perimeters equals the ratio of the areas, then 4a/4b = a2/b2; a/b = a2/b2 By cross-multiplication we get: ab2 = a2b Dividing both sides by ab we get: b = a This tells us that squares whose ratio of their perimeters equals the ratio of their areas have equal-length sides. (Side a of Square A = side b of Square B.) This appears to show, if not prove, that there are not two different-size squares meeting the condition.
What is the relationship between perimeters and areas of similar figures?
Whatever the ratio of perimeters of the similar figures, the areas will be in the ratios squared. Examples: * if the figures have perimeters in a ratio of 1:2, their areas will have a ratio of 1²:2² = 1:4. * If the figures have perimeters in a ratio of 2:3, their areas will have a ratio of 2²:3² = 4:9.
What is the width of two similar rectangles are 45 yd and 35 yd what is the ratio of the perimeters of the areas?
The ratio of their perimeters is also 45/35 = 9/7. The ratio of their areas is (9/7)2 = 81/63
If the perimeters of two squares are in a ratio of 4 to 9 what is the areas of the two squares?
The ratio is 16 to 81.
How do you find the ratio of the perimeters and areas?
There is no simple answer. For an equilateral triangle it is 6.9282/s where s is the length of each side. For a square it is 4/s A regular pentagon: 2.9062/s A regular hexagon: 2.3094/s and so on. The ratio for a circle is 2/r where r is the radius. For irregular polygons there is no rule.
What is the similarity ratio and the ratio of the perimeters of two regular octagons with areas of 18in2 and 50in2?
is it 3:5 and 3:5
If the ratio of the side lengths of two similar polygons is 31 what is the ratio of the perimeters?
Their perimeters are in the same ratio.
How do you solve the ratio perimeters of two smaller squares is 5 to 4 if the area of the smaller square is 32 square units what is the area of the larger square?
The area of similar figures is proportional to the square of any linear measurement. (And all linear measurements are directly proportional.) Thus, if the ratio of the perimeters is 5/4, the ratios of the lengths of sides is also 5/4. The ratio of the areas, on the other hand, is (5/4)2, so you can simply multiply the area of the smaller square by this factor.
