Area problems
- 1. An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:
Options- A. 1.04
- B. 2.04
- C. 3.04
- D. 4.04 Also asked in: Bank Exams, Bank PO
Correct Answer: 4.04
Explanation:
100 cm is read as 102 cm.
A1 = (100*100)Sq.cm
A2 = (102*102)Sq.cm
(A2 - A1) = = (102 + 100) x (102 - 100) = 404 sq.cm.
- 2. The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
Options- A. 16
- B. 18
- C. 20
- D. 22 Also asked in: Bank Exams, Bank PO
Correct Answer: 18
Explanation:
=> 2l + 2b = 5b => 3b = 2l
b=(2/3)l
Then, Area = 216 cm2
=> l x b = 216 => l x (2/3)l =216
l = 18 cm.
- 3. Three circles of radius 3.5cm are placed in such a way that each circle touches the other two. The area of the portion enclosed by the circles is
Options- A. 1.967
- B. 1.867
- C. 1.767
- D. 1.567 Also asked in: Bank Exams, Bank PO
Correct Answer: 1.967
Explanation:
required area = (area of an equilateral triangle of side 7 cm)- (3 * area of sector with à = 60 degrees and r = 3.5cm)
sq cm
= sq cm
= 1.967 sq cm
- 4. The dimensions of a room are 10m x 7m x 5m. There are 2 doors and 3 windows in the room. The dimensions of the doors are 1m x 3m. One window is of size 2m x 1.5m and the other 2 windows are of size 1m x 1.5m. The cost of painting the walls at Rs. 3 per sq m is
Options- A. Rs.174
- B. Rs.274
- C. Rs.374
- D. Rs.474 Also asked in: Bank Exams, Bank PO
Correct Answer: Rs.474
Explanation:
Area of 4 walls = 2(l+b)h
=2(10+7) x 5 = 170 sq m
Area of 2 doors and 3 windows = 2(1x3)+(2x1.5)+2(1x1.5) = 12 sq m
area to be planted = 170 -12 = 158 sq m
Cost of painting = Rs. 158 x 3 = Rs. 474
- 5. The ratio between the length and breadth of a rectangular field is 5 : 4 if the breadth is 20m less than the length, the perimeter of the field is :
Options- A. 260m
- B. 280m
- C. 360m
- D. none of these Also asked in: Bank Exams, Bank Clerk
Correct Answer:
- 6. Area of a square and a rectangle are equal. If side of the square is 40 cm and length of the rectangle is 64 cm, what is the perimeter of the rectangle ?
Options- A. 187 cm
- B. 178 cm
- C. 149 cm
- D. 194 cm Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 178 cm
Explanation:
Area of square = 40 x 40
= 1600 sq.cm
Given that the areas of Square and Rectangle are equal
=> Area of rectangle = 1600 Sq.cm
We know that, Area of rectangle = L x B
Given L = 64 cm
Breadth of rectangle = 1600/64 = 25 cm
Perimeter of the rectangle = 2(L + B) = 2(64+25) = 178 cm.
- 7. The base of a parallelogram is twice its height. If the area of the parallelogram is 72 sq. cm, find its height
Options- A. 6
- B. 7
- C. 8
- D. 9 Also asked in: Bank Exams, Bank PO
Correct Answer: 6
Explanation:
Let the height of the parallelogram be x. cm. Then, base = (2x) cm.
- 8. The area of a square is equal to the area of a rectangle. The length of the rectangle is 5 cm more than a side of the square and its breadth is 3 cm less than the side of the square. What is the perimeter of the rectangle ?
Options- A. 15 cm
- B. 18 cm
- C. 34 cm
- D. 26 cm Also asked in: GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 34 cm
Explanation:
Let the side of the square be 's' cm
length of rectangle = (s+5) cm
breadth of rectangle = (s-3)cm
(s+5) (s-3) =
- 5s - 3s - 15 =
2s = 15
Perimeter of rectangle = 2(L+B) = 2(s+5 + s?3) = 2(2s + 2)
= 2(15 + 2) = 34 cm
- 9. The question given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question ? Question : What is the height of a right-angled triangle ? Statements : A. The area of the triangle is 20 times its base. B. The perimeter of the triangle is equal to that of a square of the side 10 cm.
Options- A. Only statement A is required
- B. Only statement B is required
- C. Both A & B are required
- D. Neither (A) nor (B) is reuired Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: Only statement A is required
Explanation:
From statement (A),
20b = (1/2) × b × h
h = 40 cm.
- 10. A room is half as long again as it is broad. The cost of carpeting the at Rs. 5 per sq.m is Rs. 270 and the cost of papering the four walls at Rs. 10 per sq.m is Rs. 1720. If a door and 2 windows occupy 8 sq. m, find the dimensions of the room.
Options- A. b=6; l=18; H=6
- B. b=5; l=6; H=18
- C. l=6; b=18; H=15
- D. l=5; b=18; H=18 Also asked in: Bank Exams, Bank PO
Correct Answer: b=6; l=18; H=6
Explanation:
Let breadth = x metres, length = 3x metres, height = H metres.
Area of the floor=(Total cost of carpeting)/(Rate) = (270/5) sq.m = 54 sq.m
So, breadth = 6 m and length = = 9 m.
Now, papered area = (1720/10) = 172 sq.m
Area of 1 door and 2 windows = 8 sq.m
Total area of 4 walls = (172 + 8) sq.m = 180 sq.m
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