Numerical Ability Test - 14

GIVEN:

Diagonal of square = 40 cm

FORMULA USED:

Area of square = ½ (diagonal)2

CALCULATION:

According to the question,

Area of square = 1/2(40)²

⇒ 1/2 × 1600 = 800 cm²

∴ The area of the square is 800 cm2.

Given:

The area of an equilateral triangle is 10.24√3 m2

Formula used:

Area of equilateral triangle = √3/4 × a2

Perimeter of equilateral triangle = 3a

Calculation:

ATQ, √3/4 × a2 = 10.24√3 m2

⇒ a2 = 10.24 × 4

⇒ a = 3.2 × 2 = 6.4

∴ Perimeter of equilateral triangle = 3a = 3× 6.4

= 19.2 cm

Given:

BC = 25√2 cm

AB = AC

Concept used:

Pythagoras Theorem:

Hypotenuse² = Base² + Perpendicular²

Area of a triangle = (1/2) × Base × Height

For right-angled-triangle

Area of triangle = (1/2) Base × Perpendicular²

Calculation:

AB² + AC² = BC²

⇒ 2AB² = 1250

⇒ AB = 25 (Measure of sides can't take negative values)

So, the area of the triangle = (1/2) × 25 × 25 = 312.5 cm²

∴ The area of the triangle is 312.5 cm².

Given:

Length of hall = 16 m

Breadth of hall = 12 m

Formula used:

Area of rectangle = length × breadth

Calculation:

Area of hall = (16 × 12) m²

⇒ 192 m²

Now, 

LCM of 16 and 12 is 48

According to the question

Length of each square tile = (192/48) m

⇒ 4 m

∴ Required length is 4 meters

Given:

The area of rectangle = 12.46 m²

Length of the rectangle = 3.5 m

Formula used:

Area of rectangle = length × breadth

Calculation:

Let the breadth of rectangle be x

According to the question

Area of rectangle = (3.5 × x) = 12.46

⇒ 3.5x = 12.46

⇒ x = (12.46/3.5)

⇒ x = 3.56 m

∴ Required breadth of rectangle is 3.56 m

Given:

Shrinesh office floor made up of 2800 marbles

Length of floor = 3 cm = 0.03 m

Breadth of floor = 5 cm = 0.05 m

Formula used:

Area of rectangle = length × breadth

Calculation:

Area of rectangle = (0.03 × 0.05) m²

⇒ 0.0015 m²

Now,

⇒ (0.0015 × 2800) m²

⇒ 4.2 m²

Cost of polishing the floor = Rs. (25 × 4.2)

⇒ Rs. 105

∴ The cost of polishing the floor is Rs. 105

Given:

Size of bricks = 20 cm × 10 cm

The floor of hall = 16 m long and 10 m wide

Formula used:

Area of rectangle = Length × Breadth

Calculation:

Area of the floor = (16 × 10) m²

⇒ 160 m²

Area of the bricks = (20/100 × 10/100) m²

⇒ (1/5 × 1/10) m²

⇒ 1/50 m²

Now,

Number of bricks required = (160 ÷ 1/50)

⇒ (160 × 50)

⇒ 8000

∴ The required value is 8000

Given:

Parallelogram ABCD with base = (5 + 15) units

Height = 12 units 

Formula used:

Area of a parallelogram = Base × Height 

Calculation: 

Area of parallelogram ABCD = (5 + 15) × 12 

⇒ 20 × 12 

⇒ 240 sq. units

∴ The required result is 240 sq. units.

Given:

Length of rectangle = 3/5 of radius of circle

Radius of circle = Side of square with area 6400 m2

Breadth of rectangle = 15 m 

Formulas used:

Area of square = (Side)²

Perimeter of rectangle = 2(Length + Breadth) 

Calculation:

Area of square = 6400 m2

⇒ Side² = 6400 

⇒ Side = √6400 = 80 m 

Radius of cirlce = Side of square = 80 m 

⇒ Length of rectangle = 3/5 × 80 = 48 m 

∴ Perimeter of the rectangle = 2(48 + 15) m 

⇒ 126 m 

Given: 

Side of 1st square = 4 cm

Side of 2nd square = 3 cm

Formula used:

The perimeter of the square = 4 × Side

Area of the square = Side²

Calculation:

Let x be the side of the 3rd square.

According to the question,

Sum of the perimeter of two square = Perimeter of 3rd square

⇒ 4 × 9 + 4 × 12 = 4x

⇒ 4x = 4(9 + 12)

⇒ x = 21 cm

The side of third square is 21 cm.

Area of the 3^rd square = Side2

⇒ 21² = 441 cm²

∴ The area of the 3rd square is 441 cm²