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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
What is the difference between geometry and mensuration?
geometry represnt shapes and it's properties where as mensuration represents calculation of shapes like areas and perimeters.
How do you find the Area of a shaded region?
This question is too vague to have an answer, but here is one.For the shaded area (pie wedge) of a circle, find the area of the circle and multiply by the ratio of the wedge angle to the entire circle (angle/360).For the shaded region of a triangle, find the area of the smaller triangle, if necessary using trig functions to define a known angle or length of a side.For other polygons, you may be able to divide the area into triangles separately, then sum their areas.
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 squareNo, 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!
Is it true that when equilateral triangles have equal perimeters they must also have equal areas?
Yes.
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 was the most significant contribution of pi to the field of mathematics?
it has helped in finding the perimeters and areas of circle.
One equilateral triangle has sides 9 ft long Another equilateral triangle has 13 ft long Find the ratio of the areas of the triangle?
TriangleA a=90.6 TriangleB a=188.9 90.6/188.9 = .48 I think this is right, not completely sure though.
Why would two shapes have equal areas and perimeters?
There is no particular reason. In fact, in general, two shapes will have different areas or perimeters or both.
What are the properties of isosceles triangles?
All isosceles triangles: - Have angles that add up to 180 degrees - Have two equal sides. The unequal side is called the base. - Have equal base angles. - Have areas and perimeters that can be found using the formulas Area=1/2 X (base X height) and Perimeter=side+side+side An equilateral triangle with a right angle is called a right isosceles triangle. Also, all equilateral triangles are isoceles triangles, but not all isosceles triangles are right triangles.
What are the similarities between an equilateral triangle and a right triangle?
- Like all triangles, the angles must total to 180 degrees. - Both have the same formula for their areas, although the height of an equilateral triangle must be calculated from the side length. - Both have at least 2 acute angles (all three are 60 degrees in an equilateral triangle) and no obtuse angles. - Both figures have three sides. - Both figures have three angles.
What do you know about the perimeters of similar figures?
The areas are different.
What do Triangle and trapezoid have in common?
Both will individually tessellate Both are 2 dimensional shapes Both have perimeters Both have areas Both have exterior angles that add up to 360 degrees
Can a parallelogram and a rectangle have the same perimeters but different areas?
Yes.
How many feet is it around 100 acres?
You can't tell the shape or the distance around from the area. There are an infinite number of shapes and perimeters that all have areas of 100 acres. The shortest perimeter possible is a circle, with diameter (distance across) of 2,355 feet. The distance around it is 7,398 feet (about 1.4 miles). The shortest possible perimeter with straight sides is a square, 2,087 feet on every side. The distance around it is 8,348 feet (about 1.58 miles). If you stay with rectangles, there are an infinite number of different rectangles with different dimensions and different perimeters, that all have areas of 100 acres. The distance around every one of them is larger than 1.58 miles, and it can be anything up to infinity.
If the area of triangle B is 64 times greater than the area of triangle A how much greater is the perimeter of triangle B?
IF triangles 'A' and 'B' are similar (they both have the same angles),then the perimeter of 'B' is 8 times the perimeter of 'A'.If they're not similar, then the ratio of areas doesn't tell you the ratioof perimeters.
