Area Calculator
Visually calculate the area of common geometric shapes. Enter the dimensions to get the area instantly.
Area = Length × Width
How to Calculate Rectangle Area
The area of a rectangle is found by multiplying its length by its width. This formula calculates the total two-dimensional space the shape occupies.
Formula: Area = Length (l) × Width (w)
Area = Side × Side (s²)
How to Calculate Square Area
A square is a special type of rectangle where all four sides are equal. Its area is the side length multiplied by itself (squared).
Formula: Area = Side (s) × Side (s) or s²
Area = π × Radius² (πr²)
How to Calculate Circle Area
The area of a circle is calculated using its radius (the distance from the center to any point on the edge) and the mathematical constant Pi (π ≈ 3.14159).
Formula: Area = π × Radius² (πr²)
Area = ½ × Base × Height
How to Calculate Triangle Area
The area of a triangle is half of the base multiplied by its perpendicular height. The height is the distance from the base to the opposite highest point.
Formula: Area = ½ × Base (b) × Height (h)
Area = ½ × (a + b) × Height
How to Calculate Trapezoid Area
A trapezoid's area is found by averaging its two parallel bases (a and b) and multiplying that average by the height (h).
Formula: Area = ½ × (a + b) × h
Area = π × a × b
How to Calculate Ellipse Area
An ellipse's area is found by multiplying Pi (π) by its semi-major axis (a, the longest radius) and its semi-minor axis (b, the shortest radius).
Formula: Area = π × a × b
Area = Base × Height
How to Calculate Parallelogram Area
The area of a parallelogram is its base multiplied by its perpendicular height. Be careful not to use the slanted side's length.
Formula: Area = Base (b) × Height (h)
Area = (d1 × d2) / 2
How to Calculate Rhombus Area
The area of a rhombus can be easily found by multiplying the lengths of its two diagonals (d1 and d2) and then dividing the result by 2.
Formula: Area = (d1 × d2) / 2
Area = (θ/360) × πr²
How to Calculate Sector Area
A circular sector is a "slice" of a circle. Its area is a fraction of the full circle's area, determined by the sector's angle (θ) out of 360 degrees.
Formula: Area = (θ/360) × πr²
Understanding Area for Each Shape
Rectangle
A rectangle is a four-sided shape with four right angles. Its area is the product of its length and width, representing the total 2D space it covers.
Formula: Area = Length × Width
Square
A square is a special rectangle where all four sides are equal. To find its area, you simply multiply the side length by itself (i.e., square the side length).
Formula: Area = Side²
Circle
A circle's area is determined by its radius (r) and the constant Pi (π). The formula squares the radius and multiplies it by π to find the total area inside the circle.
Formula: Area = πr²
Triangle
The area of a triangle is half the product of its base and its perpendicular height. This formula works for all types of triangles, whether right, isosceles, or scalene.
Formula: Area = ½ × Base × Height
Trapezoid
A trapezoid has two parallel sides (bases 'a' and 'b'). To find its area, you average the lengths of the two bases and multiply by the perpendicular height.
Formula: Area = ½(a + b)h
Ellipse
An ellipse is like a stretched circle. Its area is calculated by multiplying Pi (π) by the product of its semi-major axis (a) and semi-minor axis (b).
Formula: Area = πab
Parallelogram
A parallelogram is a four-sided shape with two pairs of parallel sides. Its area is simply its base multiplied by its perpendicular height (not the slanted side length).
Formula: Area = Base × Height
Rhombus
A rhombus is a special parallelogram where all four sides are equal. Its area can be found by multiplying the lengths of its two diagonals and dividing by two.
Formula: Area = (d1 × d2) / 2
Sector
A sector is a 'slice' of a circle. Its area is a fraction of the full circle's area, determined by the central angle (θ) of the slice out of 360 degrees.
Formula: Area = (θ/360) × πr²
Example Problems & Solutions
Rectangle
A standard A4 paper is 21 cm wide and 29.7 cm long. What is its area?
Solution:
- Formula: Area = Length × Width
- Substitute: Area = 29.7 cm × 21 cm
- Result: Area = 623.7 cm²
Square
A standard chessboard has a side length of 40 cm. What is its total area?
Solution:
- Formula: Area = Side²
- Substitute: Area = (40 cm)²
- Result: Area = 1,600 cm²
Circle
A pizza has a radius of 15 cm. What is its total area?
Solution:
- Formula: Area = πr²
- Substitute: Area = π × (15 cm)² = 225π cm²
- Result: Area ≈ 706.86 cm²
Triangle
A yield sign is a triangle with a base of 90 cm and a height of 78 cm. What is its area?
Solution:
- Formula: Area = ½ × Base × Height
- Substitute: Area = 0.5 × 90 cm × 78 cm
- Result: Area = 3,510 cm²
Trapezoid
A plot of land has two parallel sides of 80m and 120m. The height between them is 50m. What is the area?
Solution:
- Formula: Area = ½(a+b)h
- Substitute: Area = 0.5 × (80m + 120m) × 50m
- Calculate: Area = 0.5 × 200 × 50 = 5,000 m²
- Result: Area = 5,000 m²
Ellipse
A rugby field has an elliptical shape with a semi-major axis (a) of 50m and a semi-minor axis (b) of 35m. What is its area?
Solution:
- Formula: Area = πab
- Substitute: Area = π × 50m × 35m = 1750π m²
- Result: Area ≈ 5,497.79 m²
Parallelogram
A fabric pattern is a parallelogram with a base of 10 cm and a perpendicular height of 5 cm. What is its area?
Solution:
- Formula: Area = Base × Height
- Substitute: Area = 10 cm × 5 cm
- Result: Area = 50 cm²
Rhombus
A kite is shaped like a rhombus with diagonals measuring 60 cm and 40 cm. What is its area?
Solution:
- Formula: Area = (d1 × d2) / 2
- Substitute: Area = (60 cm × 40 cm) / 2
- Result: Area = 1,200 cm²
Frequently Asked Questions
What is area?
Area is the measure of a two-dimensional space taken up by an object. It's usually measured in square units, like square meters (m²) or square feet (ft²).
Why are the diagrams included?
The diagrams provide a visual reference for the required dimensions (like length, width, or radius), making it easier to understand which numbers to enter for an accurate calculation.
What is the difference between area and perimeter?
Area is the measure of the 2D space inside a shape (measured in square units), while perimeter is the total length of the boundary around the shape (measured in linear units).
Can I calculate the area of other shapes?
This tool supports rectangles, squares, circles, triangles, trapezoids, ellipses, parallelograms, rhombuses, and sectors. We plan to add more shapes in the future based on user feedback!