Area Questions

• A square, a circle, and an equilateral triangle have the same perimeter. Consider statements: I. The square’s area is greater than the triangle’s area. II. The circle’s area is less than the triangle’s area. Which statement(s) is/are correct?
• An equilateral triangle has area x and perimeter y. Find the correct relation between x and y.
• A circle is inscribed in an equilateral triangle. The circle’s area is 154 sq. cm (use π = 22/7). Find the perimeter of the equilateral triangle.
• A rectangle has length L and breadth B with L = 2B. If the length is decreased by 5 cm and the breadth is increased by 5 cm, the area increases by “5 sq. cm more than 70 sq. cm,” i.e., by 75 sq. cm. Find the original length L.
• A rectangle’s area is 1.8 times the area of a square whose side is 20 cm. The rectangle’s length is 5 times its breadth. Find the rectangle’s perimeter.
• From a square metal plate of side 2d, circular plates of diameter d are cut without overlap. What is the maximum number of such circles that can be cut with minimum material loss?
• In a rhombus, one diagonal is 60% of the other (let the larger be D and the smaller be 0.6D). By what factor is the rhombus area compared to D^2?
• Square – side increased by 25%:\nIf each side of a square is increased by 25% (one–fourth more than the original), by what percentage does its area change overall?
• Rectangle from diagonal and perimeter:\nThe diagonal of a rectangle is 17 cm and its perimeter is 46 cm. Find the area (in sq. cm).
• Circle – radius reduced by half:\nIf the radius of a circle is decreased by 50%, what is the percentage decrease in its area?
• Parallelogram with sides 30 m and 14 m, diagonal 40 m:\nFind the area of the parallelogram.
• Rectangle sides each increased by 20%:\nBy what percentage does the area of the rectangle increase?
• Shortest route across a square plot:\nA man walks diagonally across a square instead of along two edges. Approximately what percentage distance does he save?
• Wire re-formed: circle (r = 56 cm) to square:\nA wire forms a circle of radius 56 cm. If re-bent into a square, what is the square’s area?
• Squares and their diagonals:\nFind the ratio of the area of a square to the area of the square built on its diagonal.
• Largest inscribed circle in 18 cm × 14 cm rectangle:\nFind its area (sq. cm).
• Isosceles triangle with altitude 8 cm and perimeter 32 cm:\nFind the area of the triangle.
• Triangular field cost → area → dimensions:\nThe base is three times the altitude. If cultivation costs Rs 24.68 per hectare total Rs 333.18, find base and height (in metres).
• Plastering a rectangular tank (inside walls + bottom):\nA tank is 25 m long, 12 m wide, 6 m deep. Find cost of plastering its walls and bottom at Rs 0.75 per sq. m.
• Rectangles & Parallelograms – Base twice the height:\nThe base of a parallelogram is exactly twice its height. If the area of the parallelogram is given as 338 sq cm, determine the height (in cm). Keep units standardised and show the core relation area = base * height.