Area Questions

• Rectangle — If both sides are increased by 10%, by what percentage does the diagonal increase?
• Circle — The radius is 3 cm. Find the diameter.
• Circle — The radius of a circular field is 25 m. Find its area (use A = πr^2).
• Rectangle & Perimeter from Fencing Cost — Length:breadth = 5:3. Total fencing cost is ₹ 3,000 at ₹ 7.50 per meter. Find the difference (length − breadth).
• Rectangle with Diagonal — One side is 4 m and the diagonal is 5 m. Find the area of the rectangle.
• Rectangle — If the base increases by 10% but area stays the same, by what percentage must the altitude (height) decrease?
• Hall dimensions — The length is (4/3) times its breadth. If the area is 300 sq m, find the difference (length − breadth).
• Square field — Cultivation costs ₹ 160 per hectare. Total cultivation cost is ₹ 1,440. At ₹ 0.75 per meter, what is the fencing cost around the field?
• Rectangular plot — “Half as long again” as broad (i.e., length = 1.5 × breadth). If area is 2/3 hectares, find the length (in meters).
• Rectangular field — Length:breadth = 5:4 and breadth is 20 m less than length. Find the perimeter.
• Rectangle vs Square — A rectangle of length 144 m has the same area as a square of side 84 m. Find the width of the rectangle.
• Rectangular plot — Length is four times breadth. A playground of 1,200 m2 occupies one-third of the total plot. Find the plot length (in meters).
• Walls papering cost scaling — Papering four walls of a room costs ₹ 48. In another room, each of length, breadth, and height is doubled. Find the new papering cost.
• Area of four walls — The total area of four walls is 168 sq m. Breadth is 8 m and height is 6 m. Find the length of the room.
• Area of four walls (lateral surface) of a rectangular room is 77 square meters. The room’s length = 7.5 meters and breadth = 3.5 meters. Find the height of the room (assume area of four walls = 2 * height * (length + breadth), ceiling/floor excluded).
• A rectangle has length 15 cm and area 150 cm^2, so its width is 10 cm. Only its length is increased so that the area becomes 1 1/3 times the original (i.e., 4/3 of 150 = 200 cm^2). Find the new perimeter.
• A rectangular room has length 4 meters. It can be partitioned into two equal square rooms (by building a wall along the breadth). What is the side length (and hence the partition length) of each resulting square room, in meters?
• From a square (side s), a rectangle is formed by increasing “length” by 40% and “breadth” by 30%. By what percentage does the new rectangle’s area exceed the original square’s area?
• A hall is 20 m long and 15 m broad. It is surrounded by a verandah of uniform width 2.5 m. Find the cost of flooring only the verandah at Rs 3.50 per square meter.
• Two square fields: one has area 1 hectare (10,000 m^2). The other square’s side is larger by 1%. Find the difference in their areas (in square meters).