# Area - Quantitative Aptitude

Q1. Find the area of the triangle whose sides are 9cm, 10cm and 11cm respectively

(a) 22√2 cm^{2}

(b) 25√3 cm^{2}

(c) 27√3 cm^{2}

(d) 30√2 cm^{2}

**Answer:** (d) 30√2 cm^{2}

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 cm^{2}

Q2. Find the area of the square whose diagonals is 3.2 cm long ?

(a) 4.98 cm^{2}

(b) 5.12 cm^{2}

(c) 5.23 cm^{2}

(d) 6.15 cm^{2}

**Answer:** (b) 5.12 cm^{2}

Area = ½ X diagonal^{2}

= ½ X (3.2)^{2}

= ½ X 3.2 X 3.2 cm^{2}

= 1.6 X 3.2 cm^{2}

= 5.12 cm^{2}

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 m^{2}

(b) 190 m^{2}

(c) 200 m^{2}

(d) 220 m^{2}

**Answer:** (c) 200 m^{2}

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 m^{2} = 200 m^{2}

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} cm^{2} = ½ X 32 cm^{2} = 16 cm^{2}

∴ Area of the second square = 2 X 16 cm^{2} = 32 cm^{2}

A/Q ½ X diagonal^{2} = 32

⇒ diagonal^{2} = 64

⇒ diagonal = 8 cm

Q6. The area of a square plot is 5000 m^{2}. 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 diagonal^{2}

⇒ 5000 = ½ X diagonal^{2}

⇒ diagonal^{2} = 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 = x^{2}

New side = 150 % of x = | 150 | X x = | 15x | = | 3x |

100 | 10 | 2 |

New area = | 3x | X | 3x | = | 9x^{2} |

2 | 2 | 4 |

Required ratio = | 9x^{2} |
: x^{2} = |
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 cm^{2} 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 = πr^{2}

New radius = (r + 1) cm

New Area = π(r + 1)^{2}

π(r + 1)^{2} = πr^{2} + 22

⇒ π {(r + 1)^{2} - r^{2} } = 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 m^{2}

(b) 46 m^{2}

(c) 50 m^{2}

(d) 53 m^{2}

**Answer:** (c) 50 m^{2}

Let, length = l m

breadth = b m

Now l = 2b

Diagonal^{2} = b^{2} + l^{2} = b^{2} + (2b)^{2} = b^{2} + 4b^{2} = 5b^{2}

∴ 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 m^{2} = 50 m^{2}

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