Area Questions

• Crossing a square field diagonally at 4 km/h:\nA person walks at 4 km/h and crosses a square field along its diagonal in 3 minutes (interpreting the time unit as minutes per standard usage). Find the area of the field in square metres.
• Squares – area ratio to perimeter ratio:\nGiven two squares whose areas are in the ratio 225 : 256, find the ratio of their perimeters.
• Square area 1024 sq cm → rectangle dimensions from square side:\nA square has area 1024 sq cm. Consider a rectangle whose length is twice the square’s side and whose breadth is 12 cm less than that side. Find the ratio length : breadth of the rectangle.
• Lawn 120 m × 60 m with 1.5 m inner border all around:\nA rectangular grassy plot 120 m by 60 m has a 1.5 m wide gravel path running all round on the inside. Find the cost of gravelling this path at Rs 0.65 per sq m.
• Isosceles triangle with perimeter 32 cm and equal sides 5/6 of base:\nFind the area (in cm²).
• Rectangular field ratio 5:4 and breadth 20 m less than length:\nFind the perimeter of the field (metres).
• Motorcycle speed from wheel revolutions:\nA motorcycle wheel of diameter 70 cm makes 40 revolutions in 10 seconds. Find the speed of the motorcycle in km/h.
• Two triangles – one has base 15 cm and height 12 cm; find height of a second triangle with double the area and base 20 cm:
• Circular track 14 m wide; inner circumference 440 m:\nFind the radius of the outer circle.
• Two crossing roads inside an 80 m × 60 m lawn, each 10 m wide:\nFind the cost of gravelling the roads at Rs 3 per sq m.
• Rectangle from perimeter and side difference; triangle on its diagonal:\nA rectangle has perimeter 84 m and its length is 6 m more than its breadth. Find the area of a triangle whose base equals the rectangle’s diagonal and height equals the rectangle’s length.
• Curved surface area of a hemisphere, diameter 28 cm:\nFind the curved surface area (in cm²).
• Rectangle with sides in the ratio 3:1 and perimeter 96 m:\nThe length and breadth of a rectangle are in the ratio 3 : 1. If its total perimeter is 96 m, compute the exact length (in metres) of the rectangle.
• Right triangle transformation and new hypotenuse:\nA right-angled triangle has hypotenuse 10 cm and area 24 cm^2. If the shorter leg is halved and the longer leg is doubled, find the length of the new hypotenuse.
• Circle from circumference 26.4 cm:\nWhat is the exact area (in square centimetres) of a circle whose circumference is 26.4 cm?
• Similar triangles and area removal:\nIn ΔABC, points D on AB and E on AC are such that DE ∥ BC. Given AD : DB = 2 : 5 and area(ΔABC) = 98 cm^2, find the area (in cm^2) of quadrilateral BDEC.
• Recover circumference from area:\nIf the area of a circle is 616 cm^2, compute its circumference (in centimetres).
• Largest circle inside a square of side 18 cm (repaired stem):\nA wire is used to draw the largest possible circle that fits inside a square of side 18 cm. What is the area (in cm^2) of this circle?
• Quadrilateral sides in ratio 2:3:4:5 with perimeter 280 m:\nFind the exact length (in metres) of the longest side.
• Angle chase with isosceles condition and external division:\nIn ΔABC where AC = BC and ∠ABC = 50°, extend BC to point D so that BC = CD. Find the value of ∠BAD.