A) 65.25 | B) 56.25 |

C) 65 | D) 56 |

Explanation:

let each side of the square be a , then area = ${a}^{2}$

As given that The side is increased by 25%, then

New side = 125a/100 = 5a/4

New area = ${\left(\frac{5a}{4}\right)}^{2}$

Increased area= $\frac{25{a}^{2}}{16}-{a}^{2}$

Increase %=$\frac{\left[9{a}^{2}/16\right]}{{a}^{2}}*100$ % = 56.25%

A) 48 sq units | B) 24 sq units |

C) 12 sq units | D) 6 sq units |

Explanation:

We know that,

The area of a triangle with two sides given and included angle

A =** 1/2 x product of sides x Sin(angle) **

Here the two sides are 8 & 12

Angle = 150

Area = 1/2 x 8 x 12 x sin150

Sin(150) = sin(90+60) = cos(60) = 1/2

A = 48 x 1/2 = 24

Area of the given triangle = **24 sq units.**

A) 121 sq.com | B) 154 sq.com |

C) 186 sq.com | D) 164 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**

A) 5600 sq.m | B) 1400 sq. m |

C) 4400 sq.m | D) 3600 sq.m |

Explanation:

Perimeter of the rectangle is given by 3000/10 = 300 mts

But we know,

The Perimeter of the rectangle = 2(l + b)

Now,

2(8x + 7x) = 300

30x = 300

x = 10

Required, Area of rectangle = 8x x 7x = 56 x 100 = 5600 sq. mts.

A) 333 sq.mts | B) 330 sq.mts |

C) 362 sq.mts | D) 432 sq.mts |

Explanation:

Let the breadth of the rectangle = **b mts**

Then Length of the rectangle = **b + 6 mts**

Given perimeter = 84 mts

**2(L + B) = 84 mts**

**2(b+6 + b) = 84**

2(2b + 6) = 84

4b + 12 = 84

4b = 84 - 12

4b = 72

b = 18 mts

=> Length = b + 6 = 18 + 6 = 24 mts

Now, required Area of the rectangle =** L x B = 24 x 18 = 432 sq. mts**

A) 13 | B) 9 |

C) 117 | D) 13/9 |

Explanation:

Number of square units in 13 by 9 is given by the area it forms with length and breadth as 13 & 9

Area = 13 x 9 = 117

Hence, number of square units in 13 by 9 is **117 sq.units.**

A) 97 | B) 117 |

C) 107 | D) 127 |

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.

A) 25 sq.cm | B) 16 sq.cm |

C) 9 sq.cm | D) 4 sq.cm |

Explanation:

Given length of the rectangle = 3 cm

Breadth of the rectangle = 4 cm

Then, the diagonal of the rectangle $\mathbf{D}\mathbf{}\mathbf{=}\mathbf{}\sqrt{{\mathbf{3}}^{\mathbf{2}}\mathbf{}\mathbf{+}\mathbf{}{\mathbf{4}}^{\mathbf{2}}}\mathbf{}\mathbf{=}\mathbf{}\sqrt{\mathbf{25}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{5}$

Then, it implies side of square = 5 cm

We know that Area of square **= S x S = 5 x 5 = 25 sq.cm.**

A) 5100 sq.m | B) 4870 sq.m |

C) 4987 sq.m | D) 4442 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**

${\mathbf{b}}^{\mathbf{2}}\mathbf{}\mathbf{+}\mathbf{}\mathbf{8}\mathbf{b}\mathbf{}\mathbf{+}\mathbf{}\mathbf{15}\mathbf{b}\mathbf{}\mathbf{+}\mathbf{}\mathbf{120}\mathbf{}\mathbf{=}\mathbf{}{\mathbf{b}}^{\mathbf{2}}\mathbf{}\mathbf{+}\mathbf{}\mathbf{25}\mathbf{b}$

**2b = 120**

**b = 60 m.**

**l = b + 25 = 60 + 25 = 85 m**.

Area of the floor =** 85 × 60** = **5100 sq.m**.