Online Area and Perimeter Calculator: Determine the area and the perimeter of Circle, Circle Sector, Circle Zone, Circular Ring, Ellipse, Equilateral Triangle, Hexagon, Isosceles Triangle, Parallelogram, Rectangle, Rhombus, Right Triangle, Scalene Triangle, Square and Trapezoid using our online Area and Perimeter Calculator.
To calculate the area and perimeter (circumference) of a circle, you can use the following formulas:
Area of a Circle: The formula to calculate the area of a circle is: A = πr^2 Here, "A" represents the area, and "r" represents the radius of the circle. π (pi) is a mathematical constant approximately equal to 3.14159.
Perimeter (Circumference) of a Circle: The formula to calculate the perimeter or circumference of a circle is: C = 2πr Here, "C" represents the perimeter or circumference, and "r" represents the radius of the circle. Again, π (pi) is the mathematical constant.
Please note that there are different units of measurement that can be used for radius, such as centimeters (cm), inches (in), or meters (m). Ensure that you use consistent units throughout your calculations to obtain accurate results.
Now, let's say you have the radius of the circle. You can substitute that value into the respective formulas to calculate the area and perimeter (circumference) of the circle.
To calculate the area and perimeter (circumference) of an ellipse, you can use the following formulas:
Area of an Ellipse: The formula to calculate the area of an ellipse is: A = πab Here, "A" represents the area, and "a" and "b" represent the lengths of the semi-major and semi-minor axes, respectively. π (pi) is a mathematical constant approximately equal to 3.14159.
Perimeter (Circumference) of an Ellipse: Calculating the exact perimeter of an ellipse is a complex mathematical task. However, an approximate value can be obtained using various mathematical approximations or numerical methods. One commonly used approximation is called Ramanujan's approximation, given by the formula: C ≈ π(3(a + b) - √((3a + b)(a + 3b))) Here, "C" represents the perimeter or circumference, and "a" and "b" represent the lengths of the semi-major and semi-minor axes, respectively. Again, π (pi) is the mathematical constant.
It's important to note that the perimeter of an ellipse calculated using the approximation formula may have a slight error compared to the exact value. For most practical purposes, the approximation provides a reasonable estimate of the ellipse's perimeter.
When using these formulas, ensure that you have the correct measurements of the semi-major and semi-minor axes. Additionally, use consistent units of measurement throughout your calculations to obtain accurate results.
Remember that an ellipse is a two-dimensional shape, and its perimeter refers to the total length of the outer boundary, while the area represents the space enclosed by the ellipse.
To calculate the area and perimeter of a triangle, you can use the following formulas based on the given measurements:
If you have the base (b) and the height (h) of the triangle, you can use the formula: A = (1/2) * b * h Here, "A" represents the area, "b" represents the length of the base, and "h" represents the height of the triangle.
If you have the lengths of all three sides of the triangle (a, b, c), you can use Heron's formula: A = √(s * (s - a) * (s - b) * (s - c)) Here, "A" represents the area, and "s" represents the semi-perimeter of the triangle, calculated as: s = (a + b + c) / 2
When using these formulas, ensure that you have the correct measurements of the triangle's sides, base, and height. Additionally, use consistent units of measurement throughout your calculations to obtain accurate results.
Remember that a triangle is a three-sided polygon, and the perimeter refers to the total length of all the sides, while the area represents the space enclosed by the triangle.
To calculate the area and perimeter of a regular hexagon (a polygon with six equal sides and angles), you can use the following formulas based on the given measurements:
Area of a Hexagon: The formula to calculate the area of a regular hexagon is: A = (3√3/2) * s^2 Here, "A" represents the area, and "s" represents the length of one side of the hexagon.
Perimeter of a Hexagon: The formula to calculate the perimeter of a regular hexagon is: P = 6s Here, "P" represents the perimeter, and "s" represents the length of one side of the hexagon.
When using these formulas, ensure that you have the correct measurement of the side length of the hexagon. Additionally, use consistent units of measurement throughout your calculations to obtain accurate results.
It's important to note that these formulas specifically apply to regular hexagons, where all sides and angles are equal. If you have an irregular hexagon with varying side lengths, the area and perimeter calculations will be different. In that case, you would need to determine the lengths of each side and use appropriate formulas to calculate the area and perimeter based on the shape of the irregular hexagon.
To calculate the area and perimeter of a parallelogram, you can use the following formulas based on the given measurements:
Area of a Parallelogram: The formula to calculate the area of a parallelogram is: A = base * height Here, "A" represents the area, and you need to know the length of the base and the perpendicular height of the parallelogram. The height is the perpendicular distance between the base and the opposite side.
Perimeter of a Parallelogram: The formula to calculate the perimeter of a parallelogram is: P = 2(a + b) Here, "P" represents the perimeter, and you need to know the lengths of both adjacent sides of the parallelogram. The adjacent sides are parallel and equal in length.
When using these formulas, ensure that you have the correct measurements of the base, height, and side lengths of the parallelogram. Additionally, use consistent units of measurement throughout your calculations to obtain accurate results.
It's important to note that a parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. The area represents the space enclosed by the parallelogram, while the perimeter is the total length of all the sides.
To calculate the area and perimeter of a rectangle, you can use the following formulas based on the given measurements:
Area of a Rectangle: The formula to calculate the area of a rectangle is: A = length * width Here, "A" represents the area, and you need to know the length and width of the rectangle. The length refers to the longer side, and the width refers to the shorter side.
Perimeter of a Rectangle: The formula to calculate the perimeter of a rectangle is: P = 2 * (length + width) Here, "P" represents the perimeter, and you need to know the length and width of the rectangle. The perimeter is the sum of all the sides of the rectangle.
When using these formulas, ensure that you have the correct measurements of the length and width of the rectangle. Additionally, use consistent units of measurement throughout your calculations to obtain accurate results.
It's important to note that a rectangle is a quadrilateral with opposite sides that are equal in length and all angles are right angles (90 degrees). The area represents the space enclosed by the rectangle, while the perimeter is the total length of all the sides.
To calculate the area and perimeter of a square, you can use the following formulas based on the given measurements:
Area of a Square: The formula to calculate the area of a square is: A = side^2 Here, "A" represents the area, and "side" refers to the length of one side of the square. Since all sides of a square are equal, you can simply multiply the length of one side by itself (square it) to obtain the area.
Perimeter of a Square: The formula to calculate the perimeter of a square is: P = 4 * side Here, "P" represents the perimeter, and "side" refers to the length of one side of the square. Since all sides of a square are equal, you can multiply the length of one side by 4 to obtain the perimeter, as there are four equal sides in a square.
When using these formulas, ensure that you have the correct measurement of the side length of the square. Additionally, use consistent units of measurement throughout your calculations to obtain accurate results.
It's important to note that a square is a quadrilateral with all sides of equal length and all angles being right angles (90 degrees). The area represents the space enclosed by the square, while the perimeter is the total length of all the sides.
To calculate the area and perimeter of a trapezoid, you can use the following formulas based on the given measurements:
Area of a Trapezoid: The formula to calculate the area of a trapezoid is: A = (a + b) * h / 2 Here, "A" represents the area, "a" and "b" represent the lengths of the parallel sides (the bases) of the trapezoid, and "h" represents the perpendicular height of the trapezoid. The height is the perpendicular distance between the bases.
Perimeter of a Trapezoid: The formula to calculate the perimeter of a trapezoid is: P = a + b + c + d Here, "P" represents the perimeter, and "a," "b," "c," and "d" represent the lengths of the four sides of the trapezoid. Note that in a trapezoid, the sides "a" and "c" are parallel and of equal length, and the sides "b" and "d" are non-parallel and of unequal length.
When using these formulas, ensure that you have the correct measurements of the parallel sides (bases), non-parallel sides, and height of the trapezoid. Additionally, use consistent units of measurement throughout your calculations to obtain accurate results.
It's important to note that a trapezoid is a quadrilateral with one pair of parallel sides. The area represents the space enclosed by the trapezoid, while the perimeter is the total length of all the sides.
To calculate the area and perimeter of a circle sector (also known as a circular sector), you can use the following formulas based on the given measurements:
Area of a Circle Sector: The formula to calculate the area of a circle sector is: A = (θ/360) * π * r^2 Here, "A" represents the area, "θ" represents the central angle of the sector in degrees, "π" (pi) is a mathematical constant approximately equal to 3.14159, and "r" represents the radius of the circle.
Perimeter (Arc Length) of a Circle Sector: The formula to calculate the perimeter or arc length of a circle sector is: P = (θ/360) * 2 * π * r Here, "P" represents the perimeter or arc length, "θ" represents the central angle of the sector in degrees, "π" (pi) is the mathematical constant, and "r" represents the radius of the circle.
When using these formulas, ensure that you have the correct measurement of the central angle and the radius of the circle. Additionally, use consistent units of measurement throughout your calculations to obtain accurate results.
It's important to note that a circle sector is a portion of a circle bounded by two radii and an arc. The area represents the space enclosed by the sector, while the perimeter (arc length) is the length of the curved portion of the sector.
To calculate the area and perimeter of a circle zone (also known as a circular segment), you can use the following formulas based on the given measurements:
Area of a Circle Zone: The formula to calculate the area of a circle zone is: A = (θ/360) * π * r^2 - (1/2) * r^2 * sin(θ) Here, "A" represents the area, "θ" represents the central angle of the zone in degrees, "π" (pi) is a mathematical constant approximately equal to 3.14159, and "r" represents the radius of the circle.
Perimeter (Arc Length) of a Circle Zone: To calculate the perimeter or arc length of a circle zone, you need to know the radius and the central angle of the zone. The perimeter is the length of the curved boundary of the zone.
If the central angle is less than or equal to 180 degrees, the perimeter formula is: P = (θ/360) * 2 * π * r If the central angle is greater than 180 degrees, the perimeter formula is: P = 2 * r * (π - sin(θ/2))
When using these formulas, ensure that you have the correct measurement of the central angle and the radius of the circle. Additionally, use consistent units of measurement throughout your calculations to obtain accurate results.
It's important to note that a circle zone is a portion of a circle bounded by an arc and two radii. The area represents the space enclosed by the zone, while the perimeter (arc length) is the length of the curved portion of the zone.
To calculate the area and perimeter of a circular ring (also known as an annulus), you can use the following formulas based on the given measurements:
Area of a Circular Ring: The formula to calculate the area of a circular ring is: A = π(R^2 - r^2) Here, "A" represents the area, "π" (pi) is a mathematical constant approximately equal to 3.14159, "R" represents the radius of the outer circle, and "r" represents the radius of the inner circle.
Perimeter (Circumference) of a Circular Ring: To calculate the perimeter or circumference of a circular ring, you need to know the radii of the outer and inner circles. The perimeter is the length of the curved boundary of the ring.
If you want to calculate the perimeter of the outer circle (the outer circumference), you can use the formula: P_outer = 2πR
If you want to calculate the perimeter of the inner circle (the inner circumference), you can use the formula: P_inner = 2πr
When using these formulas, ensure that you have the correct measurements of the radii of the outer and inner circles. Additionally, use consistent units of measurement throughout your calculations to obtain accurate results.
It's important to note that a circular ring is a region between two concentric circles. The area represents the space enclosed by the ring, while the perimeter (circumference) refers to the total length of the outer or inner boundary of the ring.
To calculate the area and perimeter of an equilateral triangle, you can use the following formulas based on the given measurements:
Area of an Equilateral Triangle: The formula to calculate the area of an equilateral triangle is: A = (sqrt(3) / 4) * s^2 Here, "A" represents the area, "s" represents the length of one side of the equilateral triangle, and sqrt(3) is the square root of 3.
Perimeter of an Equilateral Triangle: The formula to calculate the perimeter of an equilateral triangle is: P = 3s Here, "P" represents the perimeter, and "s" represents the length of one side of the equilateral triangle.
When using these formulas, ensure that you have the correct measurement of the side length of the equilateral triangle. Additionally, use consistent units of measurement throughout your calculations to obtain accurate results.
It's important to note that an equilateral triangle is a triangle with all three sides of equal length and all angles measuring 60 degrees. The area represents the space enclosed by the equilateral triangle, while the perimeter is the total length of all three sides.
To calculate the area and perimeter of an isosceles triangle, you can use the following formulas based on the given measurements:
Area of an Isosceles Triangle: The formula to calculate the area of an isosceles triangle is: A = (b * h) / 2 Here, "A" represents the area, "b" represents the base of the triangle, and "h" represents the height of the triangle. The base is the non-equal side, and the height is the perpendicular distance from the base to the opposite vertex.
Perimeter of an Isosceles Triangle: The formula to calculate the perimeter of an isosceles triangle is: P = 2a + b Here, "P" represents the perimeter, and "a" represents the length of the equal sides, and "b" represents the length of the base (non-equal side).
When using these formulas, ensure that you have the correct measurements of the base, equal sides, and height of the isosceles triangle. Additionally, use consistent units of measurement throughout your calculations to obtain accurate results.
It's important to note that an isosceles triangle is a triangle with two sides of equal length and two equal angles opposite those sides. The area represents the space enclosed by the isosceles triangle, while the perimeter is the total length of all three sides.
To calculate the area and perimeter of a rhombus, you can use the following formulas based on the given measurements:
Area of a Rhombus: The formula to calculate the area of a rhombus is: A = (d1 * d2) / 2 Here, "A" represents the area, and "d1" and "d2" represent the lengths of the diagonals of the rhombus. The diagonals are line segments connecting opposite vertices of the rhombus.
Perimeter of a Rhombus: The formula to calculate the perimeter of a rhombus is: P = 4 * s Here, "P" represents the perimeter, and "s" represents the length of one side of the rhombus. All sides of a rhombus are equal in length.
When using these formulas, ensure that you have the correct measurements of the diagonals or the side length of the rhombus. Additionally, use consistent units of measurement throughout your calculations to obtain accurate results.
It's important to note that a rhombus is a quadrilateral with all sides of equal length, and opposite angles are equal. The area represents the space enclosed by the rhombus, while the perimeter is the total length of all four sides.
To calculate the area and perimeter of a scalene triangle, you can use the following formulas based on the given measurements:
The semi-perimeter "s" can be calculated as: s = (a + b + c) / 2
When using these formulas, ensure that you have the correct measurements of the lengths of all three sides of the scalene triangle. Additionally, use consistent units of measurement throughout your calculations to obtain accurate results.
It's important to note that a scalene triangle is a triangle with all sides of different lengths and all angles are different. The area represents the space enclosed by the scalene triangle, while the perimeter is the total length of all three sides.
To calculate the area and perimeter of a trapezoid, you can use the following formulas based on the given measurements:
Area of a Trapezoid: The formula to calculate the area of a trapezoid is: A = (a + b) * h / 2 Here, "A" represents the area, "a" and "b" represent the lengths of the parallel sides (the bases) of the trapezoid, and "h" represents the perpendicular height of the trapezoid. The height is the perpendicular distance between the bases.
Perimeter of a Trapezoid: The formula to calculate the perimeter of a trapezoid is: P = a + b + c + d Here, "P" represents the perimeter, and "a," "b," "c," and "d" represent the lengths of the four sides of the trapezoid. Note that in a trapezoid, the sides "a" and "c" are parallel and of unequal length, and the sides "b" and "d" are non-parallel and of unequal length.
When using these formulas, ensure that you have the correct measurements of the parallel sides (bases), non-parallel sides, and height of the trapezoid. Additionally, use consistent units of measurement throughout your calculations to obtain accurate results.
It's important to note that a trapezoid is a quadrilateral with one pair of parallel sides. The area represents the space enclosed by the trapezoid, while the perimeter is the total length of all the sides.