Area problems
- 1. The diagonal of a rectangle is 41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be:
Options- A. 18
- B. 28
- C. 38
- D. 48 Also asked in: CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk
Correct Answer: 18
Explanation:
(or)
Also,
= 41 + 40 = 81
(l + b) = 9.
Perimeter = 2(l + b) = 18 cm.
- 2. The length of a rectangular hall is 5m more than its breadth. The area of the hall is 750 sq.m. The length of the hall is
Options- A. 20
- B. 25
- C. 30
- D. 35 Also asked in: CAT, Bank Exams, AIEEE, Bank PO, Bank Clerk, Analyst
Correct Answer: 30
Explanation:
Let breadth = x m
Then, length = (x+5)m
Area of a rectangle = Length x Breadth
x(x+5) = 750
x² + 5x - 750= 0
(x+30)(x-25)= 0
x = 25 or x = -30
Hence, breadth x = 25m
=> Length = x + 5 = 25 + 5 = 30m.
- 3. The length of a class room floor exceeds its breadth by 25 m. The area of the floor remains unchanged when the length is decreased by 10 m but the breadth is increased by 8 m. The area of the floor is
Options- A. 5100 sq.m
- B. 4870 sq.m
- C. 4987 sq.m
- D. 4442 sq.m Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO, IT Trainer
Correct Answer: 5100 sq.m
Explanation:
Let the breadth of floor be 'b' m.
Then, length of the floor is 'l = (b + 25)'
Area of the rectangular floor = l x b = (b + 25) × b
According to the question,
(b + 15) (b + 8) = (b + 25) × b
2b = 120
b = 60 m.
l = b + 25 = 60 + 25 = 85 m.
Area of the floor = 85 × 60 = 5100 sq.m.
- 4. 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.
- 5. 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
- 6. 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.
- 7. A circular piece of thin wire is converted into a rhombus of side 11 cm. Find the diameter of the circular piece?
Options- A. 28 cm
- B. 3.5 cm
- C. 7 cm
- D. 14 cm Also asked in: AIEEE, Bank Exams, CAT, GATE, Bank Clerk, Bank PO
Correct Answer: 14 cm
Explanation:
Circular piece is 4 x 11 = 44 cm long,
Then Circumference of circle is given by,
44 = pi x D, where D is the diameter
D = 44 / pi
Take pi = 22 / 7, then
D = 44 / (22/7) = (44 x 7) / 22
D = 14 cm.
- 8. Square units 13 by 9 of an office area is
Options- A. 97
- B. 117
- C. 107
- D. 127 Also asked in: AIEEE, Bank Exams, CAT, GATE, Analyst, Bank Clerk, Bank PO
Correct Answer: 117
Explanation:
Square units 13 by 9 of an office means office of length 13 units and breadth 9 units.
Now its area is 13x 9 = 117 square units or units square.
- 9. Find the area of the trapezium, whose parallel sides are 12 cm and 10 cm, and distance between the parallel sides is 14 cm?
Options- A. 121 sq.com
- B. 154 sq.com
- C. 186 sq.com
- D. 164 sq.com Also asked in: AIEEE, Bank Exams, CAT, Analyst, Bank Clerk, Bank PO
Correct Answer: 154 sq.com
Explanation:
We know that,
Area of trapezium = 1/2 x (Sum of parallel sides) x (Distance between Parallel sides)
= 1/2 x (12 + 10) x 14
= 22 x 14/2
= 22 x 7
= 154 sq. cm
- 10. The sides of a right-angled triangle are 12 cm, 16 cm, 20 cm respectively. A new right angle Δ is made by joining the midpoints of all the sides. This process continues for infinite then calculate the sum of the areas of all the triangles so made.
Options- A. 312 sq.cm
- B. 128 sq.cm
- C. 412 sq.cm
- D. 246 sq.cm Also asked in: AIEEE, Bank Exams, CAT, Analyst, Bank Clerk, Bank PO
Correct Answer: 128 sq.cm
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