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Area & Perimeter guide

The Area & Perimeter Calculator computes the 2D space inside a shape and the total distance around its edges. It supports rectangles, circles, triangles, and squares, providing instant results with dynamic visual feedback.

Worked examples

Calculate the area and perimeter of a rectangle

Select the "Rectangle" tab.
Enter 10 in the Length field.
Enter 5 in the Width field.
Click Calculate.

Result: Area = 50 | Perimeter = 30

Area = Length × Width (10 × 5 = 50). Perimeter = 2(Length + Width) = 2(10 + 5) = 30.

Find the circumference and area of a circle

Select the "Circle" tab.
Enter 7 in the Radius field.
Click Calculate.

Result: Area ≈ 153.938 | Circumference ≈ 43.982

Area = πr² (π × 7² ≈ 153.938). Circumference = 2πr (2 × π × 7 ≈ 43.982).

Calculate the area of a triangle using base and height

Select the "Triangle" tab.
Enter 8 as the Base.
Enter 6 as the Height.
Enter valid lengths for Side A, B, and C (e.g., 5, 6, 8).
Click Calculate.

Result: Area = 24 | Perimeter = 19

Area = ½ × Base × Height (0.5 × 8 × 6 = 24). Perimeter is the sum of the three sides (5 + 6 + 8 = 19).

Tips

•For triangles, the height must be the perpendicular distance from the base to the opposite vertex.
•The Triangle Inequality Theorem requires that the sum of any two sides must be greater than the third side.
•All results are in square units for area and linear units for perimeter.

Frequently asked questions

What is the difference between area and perimeter?

Area is the amount of 2D space inside a shape (measured in square units). Perimeter is the total distance around the outside of the shape (measured in linear units).

Why is area measured in square units?

Because it represents the number of unit squares needed to completely fill the shape.

What is the Triangle Inequality Theorem?

It states that for any valid triangle, the sum of the lengths of any two sides must be strictly greater than the length of the remaining side. If this fails, a triangle cannot exist.

How do you find the area of a triangle if you don’t know the height?

You can use Heron’s formula if you know all three sides, or use ½ab·sin(C) if you know two sides and the included angle.

What is Pi (π)?

Pi is the ratio of a circle’s circumference to its diameter. It is an irrational number approximately equal to 3.14159.

What is the radius vs. the diameter?

The radius is the distance from the center to the edge. The diameter is the distance across the circle passing through the center. Diameter = 2 × Radius.

Can a rectangle have a negative area?

No. Area and perimeter are physical measurements and must be positive numbers. The calculator rejects negative inputs.

What is a square?

A special type of rectangle where all four sides are equal in length.

How do I find the perimeter of a circle?

The perimeter of a circle is called the circumference, calculated as 2πr or πd.

What happens if I enter zero for a side length?

A shape with a side length of zero does not exist. The calculator will show an error asking for positive numbers.

What is a right triangle?

A triangle with one angle exactly equal to 90 degrees. The relationship between its sides is governed by the Pythagorean theorem.

What is an isosceles triangle?

A triangle with at least two equal sides. The angles opposite those sides are also equal.

What is an equilateral triangle?

A triangle where all three sides are equal in length, and all three angles are 60 degrees.

How do I calculate the area of a square?

Area = side × side (or side²). For a square with a side of 6, the area is 36.

Does the tool support 3D shapes?

No, this tool is strictly for 2D geometry. Volume is not calculated here.

Can I use decimals for the side lengths?

Yes. You can enter decimals (like 5.5) and the calculator will handle them.

Are the results rounded?

Results are rounded to 4 decimal places for clarity, but the internal math is precise.

Why does the triangle calculator need all three sides?

The base and height are needed for area, while all three sides are needed to calculate the perimeter.

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