Area & Perimeter Calculator

Q: What is the formula for area and perimeter of a rectangle?

Area = Length × Width. Perimeter = 2 × (Length + Width). Diagonal = √(L² + W²). Example: L=8, W=5 → Area=40, Perimeter=26, Diagonal≈9.43.

Q: How do you find the area of a triangle using Heron's formula?

Heron's formula: s = (a+b+c)/2 (semi-perimeter), Area = √(s(s−a)(s−b)(s−c)). Example: sides 3, 4, 5 → s=6, Area=√(6×3×2×1)=√36=6 sq units. You can also use Area = ½ × base × height when height is known.

Q: What is the formula for area and circumference of a circle?

Area = πr² ≈ 3.14159 × r². Circumference = 2πr ≈ 6.28318 × r. Diameter = 2r. For exam problems using π = 22/7, substitute accordingly. Example: r=7 → Area = 22/7 × 49 = 154 sq units, Circumference = 44 units.

Q: How do you calculate the area of a trapezium?

Area of Trapezium = ½ × (sum of parallel sides) × height = ½ × (a + b) × h. Perimeter = sum of all four sides = a + b + c + d. Example: parallel sides 6 and 10, height 4 → Area = ½ × 16 × 4 = 32 sq units.

Q: Where do area and perimeter questions appear in competitive exams?

Area and Perimeter questions appear in SSC CGL, CHSL, IBPS PO, Clerk, and Railway exams under the Mensuration chapter. Common question types include: finding dimensions from area/perimeter, comparing areas of two shapes, cost of fencing/carpeting a room, and combination shapes where one shape is cut from another.

Q: What is the area of a parallelogram?

Area of Parallelogram = Base × Height (perpendicular height, not slant side). Perimeter = 2 × (Base + Side). Note: height is the perpendicular distance between the parallel sides, not the slant height. Example: base=10, height=6, side=8 → Area=60, Perimeter=36.

Select Shape

Length

Width

Please enter valid positive values for Length and Width.

Side (a)

Please enter a valid positive value for Side.

Radius (r)

Please enter a valid positive value for Radius.

Enter all 3 sides for perimeter and Heron's area. Optionally enter base & height for simpler area.

Side a

Side b

Side c

Base (optional)

Height (optional)

Please enter valid side lengths. The three sides must satisfy the triangle inequality.

Base

Height (perpendicular)

Side

Please enter valid positive values for Base, Height, and Side.

a and b are the two parallel sides. c and d are the non-parallel sides.

Parallel side a

Parallel side b

Height

Side c (for perimeter)

Side d (for perimeter)

Please enter valid positive values for the two parallel sides and height.

How to Use

Select Shape

Choose the shape from the dropdown — Rectangle, Square, Circle, Triangle, Parallelogram, or Trapezium.

Enter Dimensions

Type the known measurements. All lengths should be in the same unit (cm, m, etc.).

Get Results

Click Calculate for instant area, perimeter, and additional measurements with full working.

Frequently Asked Questions

What is the formula for area and perimeter of a rectangle?

Area = Length × Width
Perimeter = 2 × (Length + Width)
Diagonal = √(L² + W²)
Example: L = 8, W = 5 → Area = 40 sq units, Perimeter = 26 units, Diagonal ≈ 9.43 units.

How do you find the area of a triangle using Heron's formula?

s = (a + b + c) / 2 (semi-perimeter)
Area = √(s(s−a)(s−b)(s−c))
Example: sides 3, 4, 5 → s = 6 → Area = √(6×3×2×1) = √36 = 6 sq units
Alternative: Area = ½ × base × height when perpendicular height is known.

What is the formula for area and circumference of a circle?

Area = πr² (π ≈ 3.14159 or use 22/7 for clean exam answers)
Circumference = 2πr
Example with r = 7 and π = 22/7: Area = 22/7 × 49 = 154 sq units, Circumference = 44 units.
Tip: Exam problems often use r = 7, 14, 21 so answers are integers with π = 22/7.

How do you calculate the area of a trapezium?

Area = ½ × (a + b) × h
where a and b are the two parallel sides and h is the perpendicular height.
Perimeter = a + b + c + d (all four sides)
Example: a = 6, b = 10, h = 4 → Area = ½ × 16 × 4 = 32 sq units.

What is the area of a parallelogram?

Area = Base × Height (perpendicular height, not slant side)
Perimeter = 2 × (Base + Side)
Example: base = 10, height = 6, side = 8 → Area = 60 sq units, Perimeter = 36 units.
Common mistake: using the slant side as height. Always use the perpendicular distance between parallel sides.

Where do area and perimeter questions appear in competitive exams?

Mensuration (area & perimeter) is a high-weight chapter in SSC CGL, CHSL, IBPS PO, Clerk, and Railway exams. Common question types: cost of fencing a field (perimeter × rate), cost of carpeting a room (area × rate), finding dimensions when perimeter or area is given, and combination problems where one shape is cut from another.

How to Use

Frequently Asked Questions

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