All questions of Area & Perimeter for RRB NTPC/ASM/CA/TA Exam

Given data:
One side of parallelogram = 8.06 cm
Perpendicular distance from opposite side = 2.08 cm

Calculating the area of the parallelogram:
To find the area of a parallelogram, we use the formula: Area = base x height

Base:
The given side of the parallelogram is considered as the base.
Base = 8.06 cm

Height:
The perpendicular distance from the opposite side is considered as the height.
Height = 2.08 cm

Area calculation:
Area = base x height
Area = 8.06 cm x 2.08 cm
Area ≈ 16.76 cm²
Therefore, the approximate area of the parallelogram is 16.76 cm². Hence, the correct answer is option 'C'.

Understanding the Problem
To find the perimeter of a triangle, we need to sum up the lengths of all three sides. In this case, the sides of the triangle are given as 6 cm, 4 cm, and 5 cm.
Calculating the Perimeter
The perimeter \( P \) of a triangle can be calculated using the formula:
\[ P = a + b + c \]
Where \( a \), \( b \), and \( c \) are the lengths of the sides.
Applying the Formula
Let's substitute the values into the formula:
- \( a = 6 \, \text{cm} \)
- \( b = 4 \, \text{cm} \)
- \( c = 5 \, \text{cm} \)
Now, calculate the perimeter:
\[ P = 6 \, \text{cm} + 4 \, \text{cm} + 5 \, \text{cm} \]
Step-by-Step Calculation
- First, add 6 cm and 4 cm:
- \( 6 + 4 = 10 \, \text{cm} \)
- Now, add the result to 5 cm:
- \( 10 + 5 = 15 \, \text{cm} \)
Final Result
Thus, the perimeter of the triangle is:
\[ P = 15 \, \text{cm} \]
Therefore, the correct answer is option 'D'.

Understanding the Problem
To find the percentage increase in the diagonals of a rectangle when its sides are increased by 5%, we start by recalling the formula for the diagonal of a rectangle. The diagonal (d) can be calculated using the Pythagorean theorem:
d = √(length² + width²)
Initial Dimensions
- Let the initial length of the rectangle be L.
- Let the initial width of the rectangle be W.
Increased Dimensions
- After a 5% increase:
- New length, L' = L + 0.05L = 1.05L
- New width, W' = W + 0.05W = 1.05W
Calculating the Initial Diagonal
- Initial diagonal, d = √(L² + W²)
Calculating the New Diagonal
- New diagonal, d' = √((1.05L)² + (1.05W)²)
- Simplifying this, we get:
- d' = √(1.1025L² + 1.1025W²)
- d' = √(1.1025(L² + W²)) = 1.05√(L² + W²)
- Thus, d' = 1.05d
Percentage Increase in Diagonal
- The increase in diagonal = d' - d = 1.05d - d = 0.05d
- Percentage increase = (Increase / Original) × 100
- Percentage increase = (0.05d / d) × 100 = 5%
Conclusion
The percentage increase in the diagonals of the rectangle is 5%. Thus, the correct answer is option C.