Area Questions

• Rectangle with breadth as a percent of length:\nThe breadth of a rectangle equals 60% of its length. If the perimeter is 800 m, find the area (in sq. m) of the field.
• Usable typing area with margins:\nA sheet is 20 cm × 30 cm (used lengthwise). Margins: 2 cm on each left/right side and 3 cm on top/bottom. What percentage of the page area is usable for typing?
• Circle relation: circumference minus semidiameter equals 37 cm.\nIf (circumference − semidiameter) = 37 cm, find the diameter of the circle (in cm).
• Wheel radius from travel distance and revolutions:\nA wheel makes 1000 revolutions while covering 88 km without slipping. Find the wheel’s radius (in metres).
• Triangle area via Heron’s formula:\nFind the area (in sq. cm) of a triangle with side lengths 26 cm, 24 cm, and 10 cm.
• Square from a rectangle’s diagonal:\nA rectangle has length 3 cm and breadth 4 cm. A square has side equal to the rectangle’s diagonal. Find the area of this square (in sq. cm).
• Fencing three sides of a rectangle:\nA rectangular field has one 20 ft side left unfenced. If the area is 680 sq. ft, how many feet of fencing are required for the other three sides?
• Rectangle with breadth 75% of length:\nThe breadth is 75% of the length. If the rectangle’s perimeter is 1050 m, find its area (in sq. m).
• Change in total area of four walls:\nRoom dimensions are in ratio L:B:H = 7:3:1. If breadth and height are doubled while length is halved, by what percent does the total area of the four walls change?
• Units in a 13 by 9 rectangle:\nHow many square units are contained in a rectangle of side lengths 13 units and 9 units?
• In two triangles, the ratio of their areas is 4 : 3.\nThe ratio of their corresponding heights is 3 : 4. What is the ratio of their corresponding bases?
• The area of a circular field is 13.86 hectares (1 hectare = 10,000 m^2).\nFind the total fencing cost at Rs 4.40 per metre (use circumference at the boundary).
• A semicircular window has diameter 63 cm.\nFind its perimeter (the curved edge plus the straight diameter).
• A triangle and a parallelogram are constructed on the same base and have equal areas.\nIf the altitude of the parallelogram is 100 m, find the altitude of the triangle.
• In an obtuse triangle, two sides have lengths 8 and 12, and the included angle is 150 degrees.\nFind the area of the triangle.
• A 120-degree sector cut from a circle has area 66/7 square centimetres.\nFind the radius of the circle.
• Floor paving cost for a rectangular room\nThe length of a room is 5.5 m and the width is 3.75 m. Calculate the total cost of paving the entire floor with slabs at the rate of ₹800 per square metre. Give the final amount in rupees (₹).
• Longest pole inside a cuboidal room\nWhat is the maximum possible length of a pole that can be placed inside a room of dimensions 12 m (length), 4 m (breadth), and 3 m (height)?
• Squares with diagonals in the ratio 2:5\nThe diagonals of two squares are in the ratio 2:5. Find the ratio of their areas.
• Equilateral triangle described on the diagonal of a square\nA square has side a. An equilateral triangle is constructed on the square’s diagonal as its side. What is the ratio of the area of the equilateral triangle to the area of the square?