Area questions ask how much surface a shape covers, or what it costs to cover or fence it.
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Q1. If the side of a square is doubled, by what factor does its area increase?
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Answer: C
Let the original side = S, so original area = S^2. Doubling gives new side = 2S, so new area = (2S)^2 = 4 x S^2. Area scales with the square of the side, so doubling the side makes the area 4 times as large.
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Q2. In Heron’s formula for the area of a triangle with sides a, b, c and semi-perimeter s = (a+b+c)/2, what is the area?
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Answer: A
Heron’s formula finds a triangle’s area from its three sides alone. First compute the semi-perimeter: s = (a+b+c)/2. Then Area = sqrt[s(s-a)(s-b)(s-c)] — the square root of that product, not the bare product.
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Q3. What is the correct formula for the area of a trapezium with parallel sides a and b, and height h, between them?
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Answer: D
Let a and b be the two parallel sides, and h the perpendicular distance between them. A trapezium’s area equals its average parallel-side length, times the height. So Area = (1/2) x (a + b) x h.
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Q4. What is the correct formula for the area of a rhombus whose diagonals are d1 and d2?
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Answer: A
A rhombus’s diagonals are perpendicular and bisect each other. This splits the rhombus into four right triangles whose combined area is (1/2) x d1 x d2. So Area = (1/2) x d1 x d2, the product of the diagonals, halved.
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Q5. What is the correct formula for the area of a circle with radius R?
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Answer: B
The area of a circle is pi times the square of its radius: Area = pi x R^2. Note that 2 x pi x R is the circumference, not the area. Squaring R (not just using R) is what makes this an area formula.
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Q6. What is the correct formula for the area of a triangle with base b and height h?
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Answer: C
A triangle is exactly half of a parallelogram with the same base b and height h. The parallelogram’s area is b x h. So the triangle’s area is (1/2) x b x h.
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Q7. What is the correct formula for the perimeter of a rectangle with length l and breadth b?
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Answer: D
Perimeter is the total length of the boundary. A rectangle has two sides of length l and two sides of length b. So perimeter = l + l + b + b = 2l + 2b = 2(l + b).
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Q8. What is the correct formula for the area of a rectangle with length l and breadth b?
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Answer: C
A rectangle’s area is the number of unit squares that cover it. Arranged in l columns and b rows, that count is l x b. So area = l x b, not the perimeter-style sum 2(l + b) or l + b.
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Q9. A room is 8 m long, 7 m wide, and 10 m high. Find the area of its four walls.
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Answer: A
Let length = L = 8 m, breadth = B = 7 m, height = h = 10 m. Area of the four walls = perimeter of the floor x height = 2 x (L + B) x h. Perimeter = 2 x (8+7) = 30 m. Area of walls = 30 x 10 = 300 sq m.
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Q10. A room is 19 m long, 16 m wide, and 6 m high. Find the area of its four walls.
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Answer: B
Let length = L = 19 m, breadth = B = 16 m, height = h = 6 m. Area of the four walls = perimeter of the floor x height = 2 x (L + B) x h. Perimeter = 2 x (19+16) = 70 m. Area of walls = 70 x 6 = 420 sq m.
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Q11. A room is 28 m long, 15 m wide, and 7 m high. Find the area of its four walls.
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Answer: C
Let length = L = 28 m, breadth = B = 15 m, height = h = 7 m. Area of the four walls = perimeter of the floor x height = 2 x (L + B) x h. Perimeter = 2 x (28+15) = 86 m. Area of walls = 86 x 7 = 602 sq m.
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Q12. A room is 22 m long, 14 m wide, and 9 m high. Find the area of its four walls.
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Answer: D
Let length = L = 22 m, breadth = B = 14 m, height = h = 9 m. Area of the four walls = perimeter of the floor x height = 2 x (L + B) x h. Perimeter = 2 x (22+14) = 72 m. Area of walls = 72 x 9 = 648 sq m.
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Q13. A room is 9 m long, 4 m wide, and 9 m high. Find the area of its four walls.
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Answer: B
Let length = L = 9 m, breadth = B = 4 m, height = h = 9 m. Area of the four walls = perimeter of the floor x height = 2 x (L + B) x h. Perimeter = 2 x (9+4) = 26 m. Area of walls = 26 x 9 = 234 sq m.
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Q14. A room is 29 m long, 16 m wide, and 9 m high. Find the area of its four walls.
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Answer: A
Let length = L = 29 m, breadth = B = 16 m, height = h = 9 m. Area of the four walls = perimeter of the floor x height = 2 x (L + B) x h. Perimeter = 2 x (29+16) = 90 m. Area of walls = 90 x 9 = 810 sq m.
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Q15. A room is 24 m long, 20 m wide, and 4 m high. Find the area of its four walls.
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Answer: A
Let length = L = 24 m, breadth = B = 20 m, height = h = 4 m. Area of the four walls = perimeter of the floor x height = 2 x (L + B) x h. Perimeter = 2 x (24+20) = 88 m. Area of walls = 88 x 4 = 352 sq m.
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Q16. A room is 28 m long, 22 m wide, and 12 m high. Find the area of its four walls.
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Answer: B
Let length = L = 28 m, breadth = B = 22 m, height = h = 12 m. Area of the four walls = perimeter of the floor x height = 2 x (L + B) x h. Perimeter = 2 x (28+22) = 100 m. Area of walls = 100 x 12 = 1200 sq m.
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Q17. A rectangular room is 15 m long and 7 m wide. Find the cost of flooring it at Rs 80 per sq m.
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Answer: D
Let length = L = 15 m, breadth = B = 7 m, rate = Rs 80 per sq m. Area of the room = L x B = 15 x 7 = 105 sq m. Cost of flooring = area x rate = 105 x 80 = Rs 8400.
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Q18. A rectangular room is 16 m long and 7 m wide. Find the cost of flooring it at Rs 50 per sq m.
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Answer: C
Let length = L = 16 m, breadth = B = 7 m, rate = Rs 50 per sq m. Area of the room = L x B = 16 x 7 = 112 sq m. Cost of flooring = area x rate = 112 x 50 = Rs 5600.
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Q19. A rectangular room is 18 m long and 16 m wide. Find the cost of flooring it at Rs 150 per sq m.
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Answer: D
Let length = L = 18 m, breadth = B = 16 m, rate = Rs 150 per sq m. Area of the room = L x B = 18 x 16 = 288 sq m. Cost of flooring = area x rate = 288 x 150 = Rs 43200.
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Q20. A rectangular room is 27 m long and 6 m wide. Find the cost of flooring it at Rs 75 per sq m.
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Answer: C
Let length = L = 27 m, breadth = B = 6 m, rate = Rs 75 per sq m. Area of the room = L x B = 27 x 6 = 162 sq m. Cost of flooring = area x rate = 162 x 75 = Rs 12150.
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Q21. A rectangular room is 24 m long and 20 m wide. Find the cost of flooring it at Rs 80 per sq m.
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Answer: A
Let length = L = 24 m, breadth = B = 20 m, rate = Rs 80 per sq m. Area of the room = L x B = 24 x 20 = 480 sq m. Cost of flooring = area x rate = 480 x 80 = Rs 38400.
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Q22. A rectangular room is 9 m long and 6 m wide. Find the cost of flooring it at Rs 150 per sq m.
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Answer: B
Let length = L = 9 m, breadth = B = 6 m, rate = Rs 150 per sq m. Area of the room = L x B = 9 x 6 = 54 sq m. Cost of flooring = area x rate = 54 x 150 = Rs 8100.
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Q23. A rectangular room is 20 m long and 10 m wide. Find the cost of flooring it at Rs 75 per sq m.
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Answer: D
Let length = L = 20 m, breadth = B = 10 m, rate = Rs 75 per sq m. Area of the room = L x B = 20 x 10 = 200 sq m. Cost of flooring = area x rate = 200 x 75 = Rs 15000.
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Q24. A rectangular room is 10 m long and 6 m wide. Find the cost of flooring it at Rs 60 per sq m.
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Answer: A
Let length = L = 10 m, breadth = B = 6 m, rate = Rs 60 per sq m. Area of the room = L x B = 10 x 6 = 60 sq m. Cost of flooring = area x rate = 60 x 60 = Rs 3600.
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Q25. A rectangular room is 27 m long and 25 m wide. Find the cost of flooring it at Rs 100 per sq m.
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Answer: C
Let length = L = 27 m, breadth = B = 25 m, rate = Rs 100 per sq m. Area of the room = L x B = 27 x 25 = 675 sq m. Cost of flooring = area x rate = 675 x 100 = Rs 67500.
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