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# Surface Area Calculator

Select the geometrical shape, enter the values, and press calculate button using 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 (**m ^{2}**). 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.

- Area of the square =
**L × L = L**^{2} - The perimeter of the square =
**4 × L** - 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**.

- Area of the Rectangle =
**L × W** - 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.

- Area of the Triangle =
**h × b** - 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.

- Area of circle =
**π × R**^{2} - Circumference of circle =
**d = 2 × π × R** - 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 **(F _{1}, F_{2})** is constant.

i.e.

**|PF _{1}| + |PF_{2}| = Constant**

- Area of ellipse =
**π × a × b** - 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.

- Area of trapezoid =
**(1/2) * (base1 + base2) * height** - 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.

- Area of parallelogram =
**b × h** - 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.

- Area of Rhombus =
**(1/2) * P * Q** - 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.

- Area of Kite =
**(1/2) * P * Q** - 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.

- Area of pentagon =
**(1/4) * √(5 * (5 + 2√5)) * a**^{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.

- Area of Hexagon =
**(3√3/2) * a**^{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.

- Area of regular octagon =
**2 * (1 + √2) * a**^{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 (R ^{2} – r^{2})**

### Sector

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

**Area of sector = 1/2π r ^{2}θ**

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 cm^{2}

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 cm^{2}

**Area of given triangle = 6 cm ^{2} **

**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 (R ^{2} – r^{2})**

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

A = 22/7(5^{2} – 3^{2})

= 22/7(25 – 9)

= (22 x 16)/7

** = 50.28 m ^{2}**