Area and Perimeter of Geometric Figures

Area and Perimeter of Geometric Figures

• Problem 25: Four cows tethered at the corners of a square field graze the maximum unshared area. To find the ungrazed area, we need to calculate the area of the square and subtract the areas grazed by each cow (which are quarter circles).
• Problem 26: A rhombus with three vertices on a circle and centre at the fourth vertex implies that the diagonals are diameters of the circle. Using the area of the rhombus (32√3 cm²) and the knowledge that the area of a rhombus is (1/2) × product of diagonals, we can find the diagonal lengths and thus the radius of the circle.
• Problem 27: An inscribed circle touches all sides of a square, while a circumscribed circle passes through all four corners. The diameter of the inscribed circle equals the side of the square. The diameter of the circumscribed circle equals the diagonal of the square. We can use the radius and the formula for the area of a circle (πr²) to calculate the areas for both inscribed and circumscribed circles.
• Problem 28: When a square is inscribed in a circle, the diagonal of the square is equal to the diameter of the circle. We can use the relationship between the side of the square and its diagonal to find the ratio of the areas of the square and the circle.
• Problem 29: An inscribed circle touches all sides of an equilateral triangle. The radius of the inscribed circle is related to the side length of the equilateral triangle. We can use the area of the inscribed circle and the formula for the area of an equilateral triangle (√3/4 * side²) to find the side length and then the perimeter.
• Problem 30: To find the number of revolutions, we first need to convert 19.8 km to centimeters. Then, we calculate the circumference of the wheel using the radius. The number of revolutions is the total distance divided by the circumference of the wheel.
• Problem 31: Calculating the distance covered in one revolution (circumference of the wheel) and the distance covered in one minute, we can find the speed in meters per minute, which can then be converted to kilometers per hour.
• Problem 32: The distance covered by the wheels equals the total distance traveled. We can calculate the circumference of the wheel, then divide the total distance by the circumference to find the number of revolutions. The diameter can be calculated using the formula for the circumference (πd).
• Problem 33: We need to convert the revolutions per minute to revolutions per second. Then, we can calculate the distance covered per second (circumference of the wheel multiplied by revolutions per second). This distance can be converted to kilometers per hour.
• Problem 34: We can calculate the required speed in centimeters per second by converting 66 km/hr to cm/sec. Then, we can calculate the distance covered per second (circumference of the wheel multiplied by revolutions per minute) and equate it to the required speed to find the revolutions per minute.
• Problem 35: We can calculate the circumference of both front and rear wheels. In 880 meters, the number of revolutions made by the front wheel is calculated by dividing the distance by its circumference.

This quiz explores the area and perimeter calculations of various geometric figures, specifically focusing on squares, rhombuses, and circles. You'll solve problems related to grazed areas of a square field and the relationship between diagonals and inscribed circles. Test your understanding of these fundamental geometric concepts!