# Area - Quantitative Aptitude

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Q21. Each side of an equilateral triangle is 42 cm. What is the area of the circle inscribed in it ?

(a) 332 cm^{2}

(b) 359 cm^{2}

(c) 423 cm^{2}

(d) 462 cm^{2}

**Answer:** (d) 462 cm^{2}

Area of the triangle = | √3 | X a^{2} = |
√3 | X 42 X 42 cm^{2} = 21 X 21 X √3 cm^{2} |

4 | 4 |

s = | 42 + 42 + 42 | = 63 |

3 |

Radius of the triangle = | Δ | = | 21 X 21 X √3 | = 7√3 |

s | 63 |

∴ Area of the circle = π r^{2} = |
22 | X 7√3 X 7√3 = 462 cm^{2} |

7 |

Q22. The length of a rectangular plot is 4½ times that of its breadth. If the area of the plot is 200 square meter, then what is its length ?

(a) 24 m

(b) 25 m

(c) 27 m

(d) 30 m

**Answer:** (d) 30 m

Let, the breadth be x m

∴ the length = 4½ X x m = ^{9x}/_{2}

A/Q x X | 9x | = 200 |

2 |

⇒ 9x^{2} = 400

⇒ x = √(^{400}/_{9}) = |
20 |

3 |

∴ Length = | 9 | X | 20 | = 30 m |

2 | 3 |

Q23. The area of a rectangle is 12 sq meters and its length is 3 times that of its breadth. What is the perimeter of the rectangle ?

(a) 16 m

(b) 19 m

(c) 21 m

(d) 24 m

**Answer:** (a) 16 m

Let, the breadth be x m

∴ the length = 3x m

A/Q x X 3x = 12

⇒ x^{2} = 4

⇒ x = 2

∴ length = 3 X 2 = 6 m

breadth = 2 m

∴ Perimeter = 2 (6 + 2) = 16 m

Q24. A road of uniform width runs round the inside of a rectangular field 38 m long and 32 m wide. If the road occupies 600 m^{2}, the width of the road is

(a) 4 m

(b) 5 m

(c) 6 m

(d) 8 m

**Answer:** (b) 5 m

Area of the field = 38 X 32 m^{2} = 1216 m^{2}

Let the width of the road be x m

∴ Area without road = (38 - 2x)(32 - 2x) m^{2} = 1216 + 4x^{2} - 140x

Area of the road = 1216 - (1216 + 4x^{2} - 140x)

⇒ 600 = 140x - 4x^{2}

⇒ 4x^{2} - 140x + 600 = 0

⇒ x^{2} - 35x + 150 = 0

⇒ (x - 30)(x - 5) = 0

∴ x = 5 m

Q25. The area of a triangle is x square cm. and its base is y cm. What is the height of the triangle ?

(a) ^{x}/_{y} cm

(b) ^{x}/_{2y} cm

(c) ^{2x}/_{y} cm

(d) ^{2x2}/_{y} cm

**Answer:** (c) ^{2x}/_{y} cm

Area = ½ X base X height

⇒ x = ½ X y X height

⇒ height = ^{2x}/_{y} cm

Q26. The two parallel sides of a trapezium are 2 cm and 4 cm respectively and the perpendicular distance between them is 3 cm. The area of the trapezium is

(a) 6 cm^{2}

(b) 7 cm^{2}

(c) 8 cm^{2}

(d) 9 cm^{2}

**Answer:** (d) 9 cm^{2}

Area = ½ X (2 + 4) X 3 cm^{2}

= ½ X 6 X 3 cm^{2} = 9 cm^{2}

Q27. What is the area of an equilateral triangle inscribed in a circle of unit radius ?

(a) ^{2√2}/_{3} sq unit

(b) ^{3√3}/_{4} sq unit

(c) ^{3√2}/_{4} sq unit

(d) ^{4√3}/_{3} sq unit

**Answer:** (b) ^{3√3}/_{4} sq unit

Let each side of the triangle be x

Now radius = ^{x}/_{√3}

⇒ 1 = ^{x}/_{√3}

⇒ x = √3

∴ Area = | √3 | X (√3)^{2} = |
√3 | X 3 = | 3√3 | sq unit |

4 | 4 | 4 |

Q28. A rectangular courtyard 3.78 m long and 5.25 m broad is to be paved exactly with square tiles, all of the same size. The minimum number of such tiles is

(a) 402

(b) 415

(c) 425

(d) 450

**Answer:** (d) 450

l = 3.78 m = 378 cm

b = 5.25 m = 525 cm

Maximum length of a square tile = H.C.F of 378, 525 = 21 cm

∴ No of tiles = | 378 X 525 | = 450 |

21 X 4 |

Q29. The perimeter of a rectangle and a square are 160 m each. The area of the recctangle is less than that of the square by 100 sq meters. The length of the rectangle is

(a) 50 m

(b) 65 m

(c) 72 m

(d) 76 m

**Answer:** (a) 50 m

Perimeter of the square = 4 X side

⇒ 160 = 4 X side

⇒ side = 40 m

Area of the square = side^{2} = 40 X 40 = 1600 squaremeter

Area of the rectangle = l X b

A/Q lb + 100 = 1600

⇒ lb = 1500

A/Q 2(l + b) = 160

⇒ l + b = 80 ------ (1)

Now, (l - b)^{2} = (l + b)^{2} - 4lb = 80^{2} - 4 X 1500 = 400

∴ l - b = 20 ------ (2)

(1) + (2) ⇒ 2l = 100 ⇒ l = 50 m

Q30. If the ratio of the areas of two squares is 16 : 1, then the ratio of their perimeter is

(a) 2:1

(b) 3:1

(c) 4:1

(d) 5:1

**Answer:** (c) 4:1

Let the area of the squares be 16x^{2}, x^{2}

∴ Each side of the 1st square = 4x

Each side of the 2nd square = x

Perimeter of the 1st square = 4 X 4x = 16x

Perimeter of the 2nd square = 4 X x = 4x

∴ Ratio of the perimeter = 16x : 4x = 4 : 1