Area - Quantitative Aptitude
Q1. Find the area of the triangle whose sides are 9cm, 10cm and 11cm respectively
(a) 22√2 cm2
(b) 25√3 cm2
(c) 27√3 cm2
(d) 30√2 cm2
Answer: (d) 30√2 cm2
Here a = 9 cm
b = 10 cm
c = 11 cm
∴ S = | 9 + 10 + 11 | cm = 15 cm |
2 |
∴ Δ = | |
√s(s-a)(s-b)(s-c) |
= | |
√15(15-9)(15-10)(15-11) |
= | |
√15 X 6 X 5 X 4 |
= 30√2 cm2
Q2. Find the area of the square whose diagonals is 3.2 cm long ?
(a) 4.98 cm2
(b) 5.12 cm2
(c) 5.23 cm2
(d) 6.15 cm2
Answer: (b) 5.12 cm2
Area = ½ X diagonal2
= ½ X (3.2)2
= ½ X 3.2 X 3.2 cm2
= 1.6 X 3.2 cm2
= 5.12 cm2
Q3. A wheel makes 1000 rotation in covering a distance of 44 km. Find the radius of the wheel ?
(a) 5.5 m
(b) 6 m
(c) 7 m
(d) 7.5 m
Answer: (c) 7 m
Distance covered in 1 rotation = | 44 km | = | 44 X 1000 | = 44 m |
1000 | 1000 |
∴ Circumference of the wheel = 44m
⇒ 2πr = 44
⇒ 2 X | 22 | X r = 44 |
7 |
⇒ r = | 44 X 7 | = 7 m |
2 X 22 |
Q4. The perimeter of a rectangle is 60 m. If its length is twice its breadth, then its area is
(a) 185 m2
(b) 190 m2
(c) 200 m2
(d) 220 m2
Answer: (c) 200 m2
Length = 2 X breadth
⇒ l = 2b
∴ Perimeter = 2 (l+b)
⇒ 60 = 2(2b+b)
⇒ 60 = 2 X 3b
⇒ b = 10 m
∴ l = 2 X 10m = 20m
∴ Area = l X b = 10 X 20 m2 = 200 m2
Q5. The diagonal of a square is 4√2 cm. The diagonal of another square whose area is double that of the first square is
(a) 7 cm
(b) 8 cm
(c) 10 cm
(d) 11 cm
Answer: (b) 8 cm
Area of the first square = ½ X (4√2)2 cm2 = ½ X 32 cm2 = 16 cm2
∴ Area of the second square = 2 X 16 cm2 = 32 cm2
A/Q ½ X diagonal2 = 32
⇒ diagonal2 = 64
⇒ diagonal = 8 cm
Q6. The area of a square plot is 5000 m2. The length of its diagonal is
(a) 75 m
(b) 90 m
(c) 100 m
(d) 120 m
Answer: (c) 100 m
Area = ½ X diagonal2
⇒ 5000 = ½ X diagonal2
⇒ diagonal2 = 10000
⇒ diagonal = 100 m
Q7. If each side of a square is increased by 50%, the ratio of the area of the resulting square to the area of the given square is
(a) 8 : 5
(b) 8 : 3
(c) 9 : 4
(d) 10 : 3
Answer: (c) 9 : 4
Let the original side be x
∴ Area = x X x = x2
New side = 150 % of x = | 150 | X x = | 15x | = | 3x |
100 | 10 | 2 |
New area = | 3x | X | 3x | = | 9x2 |
2 | 2 | 4 |
Required ratio = | 9x2 | : x2 = | 9 | : 1 = 9 : 4 |
4 | 4 |
Q8. The sides of a triangle are in the ratio ½ : 1/3 : ¼ . If the perimeter is 52 cm then the length of the smallest side is
(a) 8 cm
(b) 10 cm
(c) 11 cm
(d) 12 cm
Answer: (d) 12 cm
Ratio of sides = ½ : 1/3 : ¼ = 6 : 4 : 3
Let the sides be 6x, 4x, 3x
A/Q 6x + 4x + 3x = 52
⇒ 13x = 52
⇒ x = 4
∴ Length of the smallest side = 3 X 4 = 12 cm
Q9. The area of a circle is increased by 22 cm2 when its radius is increased by 1 cm. The original radius of the circle is
(a) 3 cm
(b) 4 cm
(c) 6 cm
(d) 7 cm
Answer: (a) 3 cm
Let the original radius be r cm
∴ Area = πr2
New radius = (r + 1) cm
New Area = π(r + 1)2
π(r + 1)2 = πr2 + 22
⇒ π {(r + 1)2 - r2 } = 22
⇒ π {(r + 1 + r)(r + 1 - r)} = 22
⇒ π {(2r + 1)} = 22
⇒ 2r + 1 = 22/π = 22/22/7 = 7
⇒ 2r = 6
⇒ r = 3 cm
Q10. The length of a rectangular plot is twice its breadth. If the length of its diagonal is 5√5 m, the area of the rectangle is
(a) 38 m2
(b) 46 m2
(c) 50 m2
(d) 53 m2
Answer: (c) 50 m2
Let, length = l m
breadth = b m
Now l = 2b
Diagonal2 = b2 + l2 = b2 + (2b)2 = b2 + 4b2 = 5b2
∴ Diagonal = √5 + b
A/Q √5 b = 5 √5
⇒ b = 5 m
∴ length = 2b = 2 X 5 = 10 m
∴ Area = l X b = 10 X 5 m2 = 50 m2
Practice Test Exam