Area problems
- 1. If length of each side of a rhombus PQRS is 8 cm and ?PQR = 120°, then what is the length (in cm) of QS?
Options- A. 4?5
- B. 6
- C. 8
- D. 12 Discuss
Correct Answer: 8
- 2. If a square and a rhombus stand on the same base, then the ratio of the areas of the square and the rhombus is:
Options- A. 1:1
- B. 1:2
- C. 1:3
- D. 1:4 Also asked in: Bank Exams, Bank PO
Correct Answer: 1:1
Explanation:
A square and a rhombus on the same base are equal in area
- 3. A rectangular parking space is marked out by painting three of its sides.If the length of the unpainted side is 9 feet, and the sum of the lengths of the painted sides is 37 feet, then what is the area of the parking space in square feet?
Options- A. 126sq.ft
- B. 120sq.ft
- C. 130sq.ft
- D. 135sq.ft Also asked in: Bank Exams, Bank PO
Correct Answer: 126sq.ft
Explanation:
Let l = 9 ft.
Then l + 2b = 37
=> 2b = 37 ? l = 37 ? 9 = 28
b = 28/2 = 14 ft.
Area = lb = 9 × 14 = 126 sq. ft.
- 4. The length of a rope in meter by which a cow must be tethered in order that she may be able to graze an area of 2826 sq.m is ?
Options- A. 15 mts
- B. 30 mts
- C. 24 mts
- D. 36 mts Also asked in: GRE, GATE, CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 30 mts
Explanation:
The cow can graze an area of 2826 sq.m i.e it is able to cover area of circle of 2826 sq.m
Therefore,
=2826
=(2826×7/22) = 899.18 = 900
r = 30 m.
Therefore, the radius of the circle implies the length of the rope = 30 mts.
- 5. An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq. m ?
Options- A. Rs. 4082.40
- B. Rs. 1024.21
- C. Rs. 2810.6
- D. Rs. 3214 Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: Rs. 4082.40
Explanation:
Length of the first carpet = (1.44)(6) = 8.64 cm
Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 x 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40
- 6. In a rectangle, length is three times its breadth. If the length and the breadth of the rectangle are increased by 30% and 100% respectively, then its perimeter increases by
Options- A. 40/3%
- B. 20%
- C. 25%
- D. 27% Also asked in: Bank Exams
Correct Answer: 25%
Explanation:
- 7. A rectangular grassy plot 110m by 65cm has a gravel path .5cm wide all round it on the inside. Find the cost of gravelling the path at 80 paise per sq.mt
Options- A. 680rs
- B. 480rs
- C. 340rs
- D. 320rs Also asked in: Bank Exams, Bank PO
Correct Answer: 680rs
Explanation:
area of theplot = 110 * 65 = 7150 sq.m
area of the plot excluding the path = (110-5)* (65-5) = 6300 sq.m
area of the path = 7150 - 6300 =850 sq.m
cost of gravelling the path = 850 x (80/100) = 680 Rs
- 8. The ratio of bases of two triangles is x:y and that of their areas is a:b. Then the ratio of their corresponding altitudes wll be
Options- A. ay:bx
- B. a:b
- C. x:y
- D. bx:ay Also asked in: Bank Exams, Bank PO
Correct Answer: ay:bx
Explanation:
a : b =(1/2 * x * H) : (1/2 * y * h)
bxH = ayh => H/h =ay/bx
Hence H:h = ay:bx
- 9. If each side of a square is increased by 25%, find the percentage change in its area.
Options- A. 56.25%
- B. 36.25%
- C. 16.25%
- D. 12.25% Also asked in: Bank Exams, Bank PO
Correct Answer: 56.25%
Explanation:
Let each side of the square be a. Then, area = .
New side =
. New area =
=
Increase in area =
Increase% =
% = 56.25%.
- 10. If the perimeters of a square and a rectangle are the same, then the area a & b enclosed by them would satisfy the condition:
Options- A. a
- B. a>b
- C. a=b
- D. none Also asked in: Bank Exams, Bank PO
Correct Answer: a>b
Explanation:
Take a square of side 4cm and a rectangle having l=6cm and b=2cm
then perimeter of square = perimeter of rectangle
area of square = 16 sq.cm
area of rectangle = 12 sq.cm
Hence a >b
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