Area Questions

• Squares – Compare areas when one square has double the diagonal of the other:\nTwo squares are given. The diagonal of the first is exactly twice the diagonal of the second. What is the ratio of their areas (larger : smaller)?
• Rectangles – Length is twice breadth, area change after adjusting sides:\nA rectangle has length equal to twice its breadth. If the length is decreased by 5 cm and the breadth is increased by 5 cm, the area increases by 75 sq cm. Find the original length.
• Circular motion – Bus wheel revolutions to maintain 66 km/h:\nThe diameter of the driving wheel of a bus is 140 cm. How many revolutions per minute must the wheel make to keep a speed of 66 km/h?
• Floor tiling – Least number of square tiles (HCF approach):\nA room 5 m 44 cm long and 3 m 74 cm broad is to be paved with identical square tiles. Find the least number of square tiles required (use consistent units).
• Heron’s formula – Triangle with sides 13 cm, 14 cm, 15 cm:\nFind the exact area (in square centimetres) of a triangle whose side lengths are 13 cm, 14 cm, and 15 cm.
• Percentage change in area – Length halved and breadth tripled:\nA rectangle has its length reduced to half and its breadth increased threefold. Find the overall percentage change in the area.
• Error propagation – Side measured 2% in excess for a square:\nIf the side of a square is measured 2% too high, what is the percentage error in the computed area?
• Three mutually touching circles (radius 3.5 cm) – Area of the central curvilinear region:\nThree equal circles of radius 3.5 cm touch each other pairwise. Find the area enclosed between the three circles (the central curved triangle).
• Rectangular field – Ratio 5:4 and breadth is 20 m less than length:\nIn a rectangle, length : breadth = 5 : 4, and the breadth is 20 m less than the length. Find the perimeter (in metres).
• Interior painting area – Exclude doors and windows:\nRoom dimensions are 10 m × 7 m × 5 m (L × B × H). Two doors of 1 m × 3 m each, one window 2 m × 1.5 m, and two windows 1 m × 1.5 m each. Find the cost to paint the walls at Rs 3 per sq m.
• Equal areas – Square vs rectangle (square side 40 cm, rectangle length 64 cm):\nA square has side 40 cm. A rectangle has the same area and length 64 cm. Find the perimeter of the rectangle.
• Equal areas – Square vs rectangle with offset sides:\nA square and a rectangle have equal area. The rectangle’s length is 5 cm more than the square’s side; its breadth is 3 cm less than the square’s side. Find the rectangle’s perimeter.
• Data sufficiency – Height of a right-angled triangle:\nQuestion: What is the height of a right-angled triangle?\nStatements:\nA) The area of the triangle is 20 times its base.\nB) The perimeter equals that of a square of side 10 cm.
• Composite costing – Carpeting vs papering a room with openings:\nA room is half as long again as it is broad (i.e., L = 1.5B). Carpeting costs Rs 5 per sq m totals Rs 270; papering four walls costs Rs 10 per sq m totals Rs 1720. A door and two windows occupy 8 sq m. Find the room dimensions (length L, breadth B, height H).
• Running around a circular field – 20 laps at 12 km/h, radius 50 m:\nA person runs around a circular field of radius 50 m at 12 km/h. How long (in minutes) will it take to complete 20 rounds?
• Cross roads inside a rectangle – Gravel cost:\nA 55 m × 35 m rectangular lawn has two 4 m wide roads crossing centrally, one along the length and one along the breadth. Find the cost of gravelling at 75 paise per sq m.
• Square fencing then inner pavement – Two-step cost:\nFencing a square field at Rs 20 per metre costs Rs 10,080. What will it cost to lay a 3 m wide pavement along the inside edge at Rs 50 per sq m?
• Room flooring cost: The length of a rectangular 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 Rs 800 per square metre. Show the computed area first and then apply the rate to obtain the final amount.
• Rectangle with given perimeter and difference: The difference between the length and breadth of a rectangle is 23 m, and its perimeter is 206 m. Find the area of the rectangle.
• Circular race track: The inner circumference of a circular track is 440 m and the track is 14 m wide uniformly. Find the radius of the outer circle of the track.