Area questions ask how much surface a shape covers, or what it costs to cover or fence it.
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Q1. A rectangular room is 28 m long and 26 m wide. Find the cost of flooring it at Rs 100 per sq m.
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Answer: B
Let length = L = 28 m, breadth = B = 26 m, rate = Rs 100 per sq m. Area of the room = L x B = 28 x 26 = 728 sq m. Cost of flooring = area x rate = 728 x 100 = Rs 72800.
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Q2. A rectangular field is 46 m long and 33 m wide. Find the cost of fencing it at Rs 20 per metre.
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Answer: A
Let length = L = 46 m, breadth = B = 33 m, rate = Rs 20 per metre. Perimeter to be fenced = 2 x (L + B) = 2 x (46+33) = 158 m. Cost of fencing = perimeter x rate = 158 x 20 = Rs 3160.
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Q3. A rectangular field is 43 m long and 7 m wide. Find the cost of fencing it at Rs 12 per metre.
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Answer: D
Let length = L = 43 m, breadth = B = 7 m, rate = Rs 12 per metre. Perimeter to be fenced = 2 x (L + B) = 2 x (43+7) = 100 m. Cost of fencing = perimeter x rate = 100 x 12 = Rs 1200.
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Q4. A rectangular field is 27 m long and 19 m wide. Find the cost of fencing it at Rs 8 per metre.
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Answer: B
Let length = L = 27 m, breadth = B = 19 m, rate = Rs 8 per metre. Perimeter to be fenced = 2 x (L + B) = 2 x (27+19) = 92 m. Cost of fencing = perimeter x rate = 92 x 8 = Rs 736.
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Q5. A rectangular field is 54 m long and 6 m wide. Find the cost of fencing it at Rs 15 per metre.
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Answer: C
Let length = L = 54 m, breadth = B = 6 m, rate = Rs 15 per metre. Perimeter to be fenced = 2 x (L + B) = 2 x (54+6) = 120 m. Cost of fencing = perimeter x rate = 120 x 15 = Rs 1800.
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Q6. A rectangular field is 57 m long and 12 m wide. Find the cost of fencing it at Rs 12 per metre.
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Answer: D
Let length = L = 57 m, breadth = B = 12 m, rate = Rs 12 per metre. Perimeter to be fenced = 2 x (L + B) = 2 x (57+12) = 138 m. Cost of fencing = perimeter x rate = 138 x 12 = Rs 1656.
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Q7. A rectangular field is 43 m long and 28 m wide. Find the cost of fencing it at Rs 25 per metre.
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Answer: B
Let length = L = 43 m, breadth = B = 28 m, rate = Rs 25 per metre. Perimeter to be fenced = 2 x (L + B) = 2 x (43+28) = 142 m. Cost of fencing = perimeter x rate = 142 x 25 = Rs 3550.
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Q8. A rectangular field is 45 m long and 33 m wide. Find the cost of fencing it at Rs 25 per metre.
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Answer: C
Let length = L = 45 m, breadth = B = 33 m, rate = Rs 25 per metre. Perimeter to be fenced = 2 x (L + B) = 2 x (45+33) = 156 m. Cost of fencing = perimeter x rate = 156 x 25 = Rs 3900.
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Q9. A rectangular field is 55 m long and 15 m wide. Find the cost of fencing it at Rs 25 per metre.
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Answer: A
Let length = L = 55 m, breadth = B = 15 m, rate = Rs 25 per metre. Perimeter to be fenced = 2 x (L + B) = 2 x (55+15) = 140 m. Cost of fencing = perimeter x rate = 140 x 25 = Rs 3500.
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Q10. A rectangular field is 16 m long and 14 m wide. Find the cost of fencing it at Rs 10 per metre.
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Answer: C
Let length = L = 16 m, breadth = B = 14 m, rate = Rs 10 per metre. Perimeter to be fenced = 2 x (L + B) = 2 x (16+14) = 60 m. Cost of fencing = perimeter x rate = 60 x 10 = Rs 600.
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Q11. A rectangular field is 53 m long and 38 m wide. Find the cost of fencing it at Rs 12 per metre.
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Answer: B
Let length = L = 53 m, breadth = B = 38 m, rate = Rs 12 per metre. Perimeter to be fenced = 2 x (L + B) = 2 x (53+38) = 182 m. Cost of fencing = perimeter x rate = 182 x 12 = Rs 2184.
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Q12. Find the area of a triangle in which two sides measure 24 cm and 60 cm, with an included angle of 30 degrees.
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Answer: A
Let the two sides be a = 24 cm and b = 60 cm, with included angle theta = 30 degrees. Area of a triangle = (1/2) x a x b x sin(theta). sin(30 deg) = 1/2. Area = (1/2) x 24 x 60 x 1/2 = 360 sq cm.
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Q13. Find the area of a triangle in which two sides measure 18 cm and 20 cm, with an included angle of 30 degrees.
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Answer: D
Let the two sides be a = 18 cm and b = 20 cm, with included angle theta = 30 degrees. Area of a triangle = (1/2) x a x b x sin(theta). sin(30 deg) = 1/2. Area = (1/2) x 18 x 20 x 1/2 = 90 sq cm.
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Q14. Find the area of a triangle in which two sides measure 26 cm and 60 cm, with an included angle of 90 degrees.
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Answer: B
Let the two sides be a = 26 cm and b = 60 cm, with included angle theta = 90 degrees. Area of a triangle = (1/2) x a x b x sin(theta). sin(90 deg) = 1. Area = (1/2) x 26 x 60 x 1 = 780 sq cm.
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Q15. Find the area of a triangle in which two sides measure 36 cm and 26 cm, with an included angle of 90 degrees.
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Answer: D
Let the two sides be a = 36 cm and b = 26 cm, with included angle theta = 90 degrees. Area of a triangle = (1/2) x a x b x sin(theta). sin(90 deg) = 1. Area = (1/2) x 36 x 26 x 1 = 468 sq cm.
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Q16. Find the area of a triangle in which two sides measure 14 cm and 8 cm, with an included angle of 90 degrees.
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Answer: A
Let the two sides be a = 14 cm and b = 8 cm, with included angle theta = 90 degrees. Area of a triangle = (1/2) x a x b x sin(theta). sin(90 deg) = 1. Area = (1/2) x 14 x 8 x 1 = 56 sq cm.
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Q17. Find the area of a triangle in which two sides measure 18 cm and 46 cm, with an included angle of 30 degrees.
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Answer: C
Let the two sides be a = 18 cm and b = 46 cm, with included angle theta = 30 degrees. Area of a triangle = (1/2) x a x b x sin(theta). sin(30 deg) = 1/2. Area = (1/2) x 18 x 46 x 1/2 = 207 sq cm.
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Q18. Find the area of a triangle in which two sides measure 14 cm and 24 cm, with an included angle of 30 degrees.
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Answer: C
Let the two sides be a = 14 cm and b = 24 cm, with included angle theta = 30 degrees. Area of a triangle = (1/2) x a x b x sin(theta). sin(30 deg) = 1/2. Area = (1/2) x 14 x 24 x 1/2 = 84 sq cm.
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Q19. Find the area of a triangle in which two sides measure 46 cm and 46 cm, with an included angle of 90 degrees.
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Answer: A
Let the two sides be a = 46 cm and b = 46 cm, with included angle theta = 90 degrees. Area of a triangle = (1/2) x a x b x sin(theta). sin(90 deg) = 1. Area = (1/2) x 46 x 46 x 1 = 1058 sq cm.
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Q20. Find the area of a triangle in which two sides measure 18 cm and 18 cm, with an included angle of 90 degrees.
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Answer: D
Let the two sides be a = 18 cm and b = 18 cm, with included angle theta = 90 degrees. Area of a triangle = (1/2) x a x b x sin(theta). sin(90 deg) = 1. Area = (1/2) x 18 x 18 x 1 = 162 sq cm.
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Q21. Find the area of a triangle in which two sides measure 16 cm and 56 cm, with an included angle of 90 degrees.
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Answer: B
Let the two sides be a = 16 cm and b = 56 cm, with included angle theta = 90 degrees. Area of a triangle = (1/2) x a x b x sin(theta). sin(90 deg) = 1. Area = (1/2) x 16 x 56 x 1 = 448 sq cm.
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Q22. Find the area of a triangle in which two sides measure 34 cm and 24 cm, with an included angle of 90 degrees.
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Answer: C
Let the two sides be a = 34 cm and b = 24 cm, with included angle theta = 90 degrees. Area of a triangle = (1/2) x a x b x sin(theta). sin(90 deg) = 1. Area = (1/2) x 34 x 24 x 1 = 408 sq cm.
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Q23. Find the area of a triangle in which two sides measure 50 cm and 58 cm, with an included angle of 30 degrees.
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Answer: A
Let the two sides be a = 50 cm and b = 58 cm, with included angle theta = 30 degrees. Area of a triangle = (1/2) x a x b x sin(theta). sin(30 deg) = 1/2. Area = (1/2) x 50 x 58 x 1/2 = 725 sq cm.
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Q24. Find the area of a triangle in which two sides measure 38 cm and 8 cm, with an included angle of 30 degrees.
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Answer: B
Let the two sides be a = 38 cm and b = 8 cm, with included angle theta = 30 degrees. Area of a triangle = (1/2) x a x b x sin(theta). sin(30 deg) = 1/2. Area = (1/2) x 38 x 8 x 1/2 = 76 sq cm.
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Q25. Find the area of a triangle in which two sides measure 60 cm and 32 cm, with an included angle of 30 degrees.
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Answer: D
Let the two sides be a = 60 cm and b = 32 cm, with included angle theta = 30 degrees. Area of a triangle = (1/2) x a x b x sin(theta). sin(30 deg) = 1/2. Area = (1/2) x 60 x 32 x 1/2 = 480 sq cm.
Related topics: Area: Formulas, Shortcuts and Solved Examples