Area problems
- 1. Find the area of the square whose side is equal to the diagonal of a rectangle of length 3 cm and breadth 4 cm.
Options- A. 25 sq.cm
- B. 16 sq.cm
- C. 9 sq.cm
- D. 4 sq.cm Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO, IT Trainer
Correct Answer: 25 sq.cm
Explanation:
Given length of the rectangle = 3 cm
Breadth of the rectangle = 4 cm
Then, the diagonal of the rectangle
Then, it implies side of square = 5 cm
We know that Area of square = S x S = 5 x 5 = 25 sq.cm.
- 2. A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required?
Options- A. 44ft
- B. 88ft
- C. 22ft
- D. 11ft Also asked in: Bank Exams, Bank PO
Correct Answer: 88ft
Explanation:
Given that length and area, so we can find the breadth.
Length x Breadth = Area
=> 20 x Breadth = 680
=> Breadth = 34 feet
Area to be fenced = 2B + L = 2 (34) + 20 = 88 feet
- 3. The breadth of a rectangular field is 75% of its length. If perimeter of the field is 1050 m, what will be th area of field ?
Options- A. 65700 sq.m
- B. 54500 sq.m
- C. 78700 sq.m
- D. 67500 sq.m Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 67500 sq.m
Explanation:
Let the length be 'l' and breadth be 'b'.
b = l × 3/4__________(a)
2(l+b) = 1050
l+b = 525___________(b)
From equations (a) and (b),
l = 300m, b = 225 m
Area = l × b
= 300 × 225
= 67500 sq.m.
- 4. The length, breadth and height of a room are in the ratio 7:3:1. If the breadth and height are doubled while the length is halved, then by what percent the total area of the 4 walls of the room will be increased ?
Options- A. 90%
- B. 88%
- C. 85%
- D. 84% Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 90%
Explanation:
Let length, breadth and height of the room be 7, 3, 1 unit respectively.
Area of walls = 2(l+b)xh = 2(7+3)x1 = 20 sq. unit.
Now, length, breadth and height of room will become 3.5, 6 and 2 respectively.
Area of walls = 2(l+b)xh = 2(3.5+6)x2 = 38 sq. unit.
% Increase in the area of walls = (38-20)x100/20 = 90%.
- 5. How many square units in 13 by 9?
Options- A. 13
- B. 9
- C. 117
- D. 13/9 Also asked in: AIEEE, Bank Exams, CAT, Analyst, Bank Clerk, Bank PO
Correct Answer: 117
Explanation:
Number of square units in 13 by 9 is given by the area it forms with length and breadth as 13 & 9
Area = 13 x 9 = 117
Hence, number of square units in 13 by 9 is 117 sq.units.
- 6. Find the area of a square, one of whose diagonals is 3.8 m long
Options- A. 7.22
- B. 6.22
- C. 4.22
- D. 3.22 Also asked in: Bank Exams, Bank PO
Correct Answer: 7.22
Explanation:
Area of the square =
- 7. In two triangles, the ratio of the areas is 4 : 3 and the ratio of their heights is 3 : 4. Find the ratio of their bases.
Options- A. 13:9
- B. 16:9
- C. 15:9
- D. 14:9 Also asked in: Bank Exams, Bank PO
Correct Answer: 16:9
Explanation:
Let the bases of the two triangles be x and y and their heights be 3h and 4h respectively.
Then,
Required ratio = 16 : 9.
- 8. The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.40 per metre.
Options- A. 2808
- B. 3808
- C. 4808
- D. 5808 Also asked in: Bank Exams, Bank PO
Correct Answer: 5808
Explanation:
Area = (13.86 x 10000) sq.m = 138600 sq.m
Circumference =
Cost of fencing = Rs. (1320 x 4.40) = Rs. 5808.
- 9. A semicircular shaped window has diameter of 63cm. Its perimeter equals
Options- A. 162
- B. 132
- C. 142
- D. 172 Also asked in: Bank Exams, Bank PO
Correct Answer: 162
Explanation:
perimeter of window = r+2r
= [(22/7) x (63/2) + 63] = 99+63 = 162 cm
- 10. A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m , then the altitude of the triangle is
Options- A. 200m
- B. 300m
- C. 400m
- D. 100m Also asked in: Bank Exams, Bank PO
Correct Answer: 200m
Explanation:
Let the triangle and parallelogram have common base b,
let the Altitude of triangle is h1 and of parallelogram is h2(which is equal to 100 m), then
Area of triangle =
Area of rectangle = b*h2
As per Given,
h1=200
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