Area problems
- 1. 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 Discuss
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
- 2. The area of a square field is 69696sq.cm..its diagonal will be equal to
Options- A. 373
- B. 573
- C. 473
- D. 673 Discuss
Correct Answer: 373
Explanation:
- 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 Discuss
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 area of a field in the shape of a trapezium measures 1440sq m. The perpendicular distance between its parallel sides is 24cm. If the ratio of the sides is 5:3, the length of the longer parallel side is:
Options- A. 75
- B. 85
- C. 95
- D. 105 Discuss
Correct Answer: 75
Explanation:
Area of field = = 96x sq.m
96x = 1440 => x = = 15
Hence, the length of longer parallel side = 5x = 75m
- 5. A rectangular paper when folded into two congruent parts had a perimeter of 34cm foer each part folded along one set of sides and the same is 38cm. When folded along the other set of sides. What is the area of the paper?
Options- A. 140
- B. 150
- C. 160
- D. 170 Discuss
Correct Answer: 140
Explanation:
when folded along the breadth
we have 2(l/2 +b) = 34 or l+2b = 34...........(1)
when folded along the length, we have 2(l+b/2)=38 or 2l+b =38.....(2)
from 1 &2 we get l=14 and b=10
Area of the paper = 14*10 = 140 sq cm
- 6. The perimeter of a square is 40 meters. Find the length of one side of the square
Options- A. 10m
- B. 20m
- C. 30m
- D. 40m Discuss
Correct Answer: 10m
Explanation:
P = 4 x s
- 7. The perimeter of a rectangle is 160 cm. The rectangle is 4 times longer than wide. What are the length and width of this rectangle?
Options- A. l=65;b=16
- B. l=16;b=64
- C. l=64;b=16
- D. l=16;b=48 Discuss
Correct Answer: l=64;b=16
Explanation:
P=2(l+b)
l=4b
- 8. A 3 by 4 rectangle is inscribed in circle. What is the circumference of the circle?
Options- A. 2.5?
- B. 3?
- C. 5?
- D. 4? Discuss
Correct Answer: 5?
Explanation:
Draw the diagram. The diagonal of the rectangle is the diameter of the circle. The diagonal is the hypotenuse of a 3,4,5 triangle and is therefore, 5.
Circumference = ?.diameter = 5?
- 9. A triangle has a perimeter 13. The two shorter sides have integer lengths equal to x and x + 1. Which of the following could be the length of the other side?
Options- A. 4
- B. 6
- C. 8
- D. None of the above Discuss
- Option A cannot be correct because 4 would not be the longest side.(sides 4, 5, and 4)
- Option B could be correct because the other two sides would be 3 and 4.
- Option C cannot be correct because this third side would be greater than the sum of the other two sides.
Correct Answer: 6
Explanation:
The measure of the third side of a triangle must lie between the sum and the difference of the other two sides. Using this fact along with the answer choices, we can eliminate the wrong answers.
- 10. 2 metres broad pathway is to be constructed around a rectangular plot on the inside. The area of the plots is 96 sq.m. The rate of construction is Rs. 50 per square metre. Find the total cost of the construction?
Options- A. 20
- B. 30
- C. 40
- D. data is inadequate Discuss
Correct Answer: data is inadequate
Explanation:
Given lb =96
Area of pathway = [(l-4)(b-4)-lb] = 16-4(l+b)
Which cannot be determined. so, data is inadequate.
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