Surface Area Calculator

Surface Area Calculator

Surface area calculator is used to calculate the area, perimeter, side, and diagonal of two-dimensional shapes. The surface area calculator gives step-by-step solutions with its formulas in a few seconds.

The surface area of two-dimensional shapes

The surface area of 2D is defined as “The measurement of the total area that is enclosed in a flat surface”. 2D shapes are flat shapes that have only length and width. The unit of area is a square meter (m²). Examples of 2D shapes are circles, triangles, squares, rectangles, etc.

Formulas for two-dimensional shape

We will discuss many two-dimensional shapes with formulas. Let’s discuss 2D shapes one by one.

Square

In the square, the length and angle of all four sides are equal, and each angle is 90 degrees.

1. Area of the square = L × L = L²
2. The perimeter of the square = 4 × L
3. The diagonal of the square = L

Where 

• L is the length of one side of the square

Rectangle

In a rectangle, the length of opposite sides and all angles are equal, and each angle is 90 degrees.

1. Area of the Rectangle = L × W
2. The perimeter of the Rectangle = 2 (L + W)

Where

• L is the length of the rectangle
• W is the width of the rectangle

Triangle

Triangle contains three sides, three angles, and three edges.

1. Area of the Triangle =  h × b
2. The perimeter of the Triangle = a + b + c

Where

• b is the base of the triangle.
• h is the height of the triangle.
• a & c are the other sides of the triangle.

Circle

A circle is a flat plane that has no edge.

1. Area of circle = π × R²
2. Circumference of circle = d = 2 × π × R
3. Diameter of circle = 2 × R

Where

• R is the radius of the circle
• d is the diameter of the circle
• π is equal to 22/7

Ellipse

In an ellipse, the sum of the distance from any point on the ellipse to fixed points (F₁, F₂) is constant.

i.e.  

|PF₁| + |PF₂| = Constant

1. Area of ellipse = π × a × b
2. Circumference of ellipse = π * (3(a + b) - √((3a + b) * (a + 3b)))

Where

• a is the major axis (lies on the x-axis)
• b is the minor axis (lies on the y-axis)
• π is equal to 22/7

Trapezoid

At least one pair of sides in the trapezoid is parallel. It has four straight lines with unequal lengths. Other name of trapezoid is trapezium.

1. Area of trapezoid = ­ (1/2) * (base1 + base2) * height
2. Perimeter of trapezoid = a + b + c + d

Where

• Sides b and a are bases of a trapezium
• h is a height  of a trapezium
• c & d sides are not parallel sides of a trapezium

Parallelogram

The sides of a parallelogram are parallel and equal. Opposite angles are also equal.

1. Area of parallelogram = b × h
2. Perimeter of parallelogram = 2 (a + b)

Where

• h is the height of the parallelogram
• b is base of the parallelogram
• a is other lengths of the parallelogram

Rhombus

Rhombus has four equal sides with equal lengths. The other name for rhombus is diamond.

1. Area of Rhombus =  (1/2) * P * Q
2. Perimeter of rhombus = a + a + a + a = 4a

Where

• P and Q are diagonals
• a is the length of a rhombus.

Kite

Kite is a flat closed shape having four straight lines with equal adjacent sides.

1. Area of Kite =   (1/2) * P * Q
2. Perimeter of kite = 2 (a + b)

Where

• P and Q are diagonals,
• a & b are the lengths of a kite.

Regular pentagon

A regular pentagon has five sides with equal lengths and five equal angles. Each interior angle measures 108 degrees and the sum of the interior angle of a regular pentagon is 540 degrees.

1. Area of pentagon = (1/4) * √(5 * (5 + 2√5)) * a²
2. Perimeter of pentagon = a + a + a + a + a = 5a

Where

• d is the diagonal of the pentagon,
• a is the length of each side of the pentagon.

Regular Hexagon

A regular hexagon has six sides with equal lengths and six equal angles. Each interior angle measures 120 degrees and the sum of the interior angle of the pentagon is 720 degrees.

1. Area of Hexagon =  (3√3/2) * a²
2. Perimeter of Hexagon = a + a + a + a + a + a = 6a

Regular octagon

A regular octagon has eight equal sides and angles. The total interior angle of a regular octagon is 1080degree and its total exterior angle is 360 degrees.

1. Area of regular octagon = 2 * (1 + √2) * a²
2. Perimeter of regular octagon = a + a + a + a + a + a + a + a = 8a

Where

• a is the length of the side of a given regular octagon.

Annulus (Ring)

The area between two circles having the same center is known as an annulus or ring.

O is the Center of both circles, R is the radius of the outer circle, and r is the radius of the inner circle.

Area of annulus (Ring) = π (R² – r²)

Sector

The region between two radiuses with an arc is called a sector.

Area of sector = 1/2π r²θ

Where r is the radius and is the subtended angle between two radii.

How to find surface area?

Example 1

Find the Area and perimeter of a given parallelogram

Solution

Step 1:  Identify the height and base. Here

b = 3 cm

h = 4 cm

a = 2cm

Step 2: write the formulas of a parallelogram

Area of parallelogram = b × h

Perimeter of parallelogram = 2 (a + b)

Step 3: Put the given value in formulas, and simplify

Area of parallelogram = 3 cm × 4 cm = 12 cm²

Perimeter of parallelogram = 2 (2 cm + 3 cm)

                                                   = 2 (5 cm)

                                                   = 10 cm

Example 2

Find the area of the given triangle.

Solution

Here;

Base = 3 cm

Height = 4 cm

Area of triangle = 1/2 (base x height)

                              = 1/2 (3 x 4)

                               = 0.5 × 12 cm²

Area of given triangle = 6 cm²                                

Example 3

Find the Area between two circles having the same center, when the radius of the outer circle is 5 m and the radius of the inner circle is 3 m.

Solution

Radius of outer circle = R = 5 m

Radius of inner circle = r = 3 m

Also, π = 22/7

As we know that

Area of annulus = π (R² – r²)

Put the given value in the formula, and we get,

A =  22/7(5² – 3²)

    =  22/7(25 – 9)

    = (22 x 16)/7

    = 50.28 m²