1.A wire shaped into a square encloses an area of 484 square centimeters. If the same wire is reshaped into a circle, what will be the area enclosed by the circle?
2.A circular field and a square field have the same perimeter. If the area of the square field is 12,100 m², what is the area of the circular field?
3.A circular field and a square field have the same perimeter. If the area of the square field is 484 square meters, what is the diameter of the circular field?
4.What is the area of the biggest circle that fits inside a rectangle measuring 18 cm by 14 cm?
5.If the radius of a circle is tripled, by what factor does its circumference increase?
6.If the radius of a circle is increased by 1 cm, the area grows by 22 square centimeters. What was the circle's original radius?
7.The radius of the larger circle exceeds that of the smaller circle by 7 cm. If the difference in their areas is 1078 square centimeters, what is the radius of the smaller circle?
8.If a circle has an area of 24.64 square meters, what is its circumference?
9.A square field has an area of 6050 square meters. What is the length of its diagonal?
10.By what percentage does the area of a square increase if each side length is enlarged by 25%?
11.A rhombus has an area of 2016 square centimeters and each side measures 65 centimeters. What are the lengths of its diagonals?
12.What is the maximum possible area of a triangle that can be inscribed inside a semicircle with radius R cm?
13.A typist has a sheet of paper measuring 30 cm by 15 cm. He leaves margins of 2.5 cm at the top and bottom, and 12.5 cm on both the left and right sides. Approximately what percentage of the paper's total area remains available for typing?
14.Two triangles are similar, with areas measuring 12 cm² and 48 cm² respectively. If the height of the smaller triangle is 2.1 cm, what is the height of the larger triangle corresponding to it?
15.If the height of a triangle is reduced by 40% while its base is increased by 40%, how will the area of the triangle be affected?
16.The sides of a triangle are proportional to 1/2, 1/3, and 1/4. If the triangle's perimeter measures 52 cm, what is the length of its shortest side?
17.Given that a circle, a square, and an equilateral triangle all have the same area, which shape has the largest perimeter?
18.A rectangle with sides measuring 18 cm and 26 cm has the same perimeter as a circle. What is the area of that circle?
19.If the length of each side of a square is increased by 50%, what is the ratio of the new square's area to the original square's area?
20.If the length of a rectangle is increased by 20% while its width is reduced by 20%, what happens to its area?