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# Plane Shape|Definition & Meaning

## Definition

Any two-dimensional or “flat” shape is called a **plane** shape. A plane has** length** and width but no** thickness**, which is true for** all t**wo-dimensional shapes as well. Therefore, we call them **plane shapes.** Examples include rectangles, triangles,** circles**, ellipses, etc.

## What Is a Plane Shape?

In mathematics, a plane shape is a 2-dimensional **flat** shape with no **thickness**. It is also known as a** plane figure** or 2-dimensional **shape**. The term 2-dimensional refers to the** fact** that these shapes have **length** and **width**.

A plane shape may be a **combination** of sides and **corners**. Some plane shapes are **square**, rectangle, circle, **triangle**, rhombus, etc.

## Sides and Corners of Plane Shapes

Plane shapes are a combination of **sides** and **corners**. The line segment that makes up a **plane** shape is called the **side**. The **point** where the two sides **assemble** is called the **corner**.

Different plane shapes have **different** numbers of sides and corners; for **example,** rectangles and **squares** have 4 sides and 4 corners, whereas a **triangle** has 3 sides and 3 corners.

## Types of a Plane Shape

There are two types of plane shapes, i.e., **open** and **closed** shapes.

### Closed Plane Shapes

The 2 dimensional flat, **closed** surfaces are called closed shapes. They have **sides**, corners, and **faces** and are joined by line **segments**. In our daily life, we see many examples of **closed-plane** shapes, such as a cookie, **chess** boards, currency notes, **books**, laptops, balls, slices of pizza, **bricks**, and many more. There are many kinds of plane **shapes**. Here, we will discuss a few of them.

- Square
- rectangle
- circle
- Triangle
- Pentagons
- Hexagons
- Rhombus
- Trapezoids
- Parallelogram

#### Square

A square is a flat, **2-dimensional** plane shape with 4 sides, 4 **corners**, and 4 faces. Its construction comprises four line segments joined together. All **four** sides are equal in **length**. It has four right **angles**. Diagonals **bisect** each other at **90 degrees**. If a **four-sided** shape has equal sides and right **angles** at corners, that’s a **square**.

Some daily life **squares** are a chess board, **pizza** box, **keyboard** keys, photo frame, bread, Rubik’s cube, **cheese** slice, etc.

#### Rectangle

A rectangle is a flat, 2-dimensional plane **shape** with 4 sides, 4 **corners**, and 4 faces, but it **differs** from a square. **How**? A rectangle has **unequal** sides, but opposite sides are equal and **parallel** to each other. It has four **right** angles at the **corners**.

A **rectangle** has 2 **diagonals** that bisect each other and are **equal** in length. Some examples of rectangles are **blackboards**, television, mobile phone, currency note, books, **laptops**, doors, a sheet of paper, etc.

#### Circle

A circle is a plane shape with no **corners**; rather, it only has a **curved** boundary. It is a set of **points** that are at a fixed **distance** from the **center**. It has no sides, no corners, and no **diagonals**. The line segment that **divides** a circle into two halves is the **diameter**.

Some examples of **circles** are football, **round** wall clock, pizza, **wheel**, rings, cake, buttons, CDs, full moon, etc.

#### Triangle

A **triangle** is a 2-dimensional **plane** shape with 3 sides, 3 **corners**, and 3 **angles**. The angles and **sides** of a triangle may or may not be **equal** depending on the **type** of triangle. The 3 angles of a triangle give a total of 180 degrees.

Acute **triangles**, **obtuse** triangles, **isosceles** triangles, right angle triangles, etc., are some types of triangles. Daily life examples of **triangles** are slices of **pizza**, sign boards, sandwiches, etc.

#### Pentagon

A pentagon is a **five-sided** 2-dimensional plane shape. It is a type of **polygon** with 5 **corners**. It has 5 angles which makes a total of 540 degrees. A **pentagon** has 5 **diagonals**. Daily life **examples** of a pentagon are cupcakes, diamonds, etc.

#### Hexagon

A hexagon is a **flat** 2-dimensional plane shape with 6 sides, 6 **corners**, and 6 angles. A **regular** hexagon has all the sides equal in length. All the **interior** angles of a **regular** hexagon measures **120 degrees,** and all the **exterior** angles measure **60 degrees**.

It has 6 lines of **symmetry** and 6 angles of **rotation**. Real-life hexagons are **honeycombs**, nuts, tie knots, white divisions of a **volleyball**, etc.

#### Rhombus

A rhombus is a **plane** shape having all 4 sides equal and **opposite** sides **parallel**. In a rhombus, the angles opposite to each other are equal in length. **Diagonals** of a rhombus **bisect** each other **perpendicularly**.

#### Trapezium

A trapezium is a 2-dimensional plane **shape** with 4 **sides** and one pair of **parallel** sides. The parallel sides are known as **bases**, and the **non-parallel** sides are **legs**. Right trapezium, **isosceles** trapezium, and **scalene** trapezium are the 3 types of trapeziums. If we add all the angles of a trapezium, it gives us a total of 360 degrees.

#### Parallelogram

A Parallelogram is a plane shape with **opposite** sides equal and parallel. Diagonals of a **parallelogram** are unequal in length and bisect each other at the **midpoint**. A parallelogram has **opposite** equal angles.

### Area and Perimeter of Closed Shapes

The area of the plane shape is the entire region **surrounded** by the **boundary** of the figure in a **2-dimensional** plane. Perimeter is the path **covered** by the boundary in a 2-dimensional plane.

The area and perimeter of some plane shapes are as follows:

**Square**

Area of square = a$^2$

Perimeter of square = 4a

**Rectangle **

Area of rectangle = a x b

Perimeter of rectangle = 2(a+b)

**Circle**

Area of circle= pie.r$^2$

Perimeter/circumference of circle = 2pie.r

**Triangle **

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

The perimeter of the triangle= sum of all sides

**Pentagon**

Area of pentagon= 1\2(perimeter x apothem)

The perimeter of a pentagon= 5 x sides

**Hexagon**

Area of hexagon = 1\2(perimeter x apothem)

The perimeter of the hexagon =6 x sides

**Rhombus**

Area of rhombus = 1\2(product of diagonals)

The perimeter of the rhombus = 4 x side

**Trapezium**

Area of trapezium = 1\2 x (a+b) x h

The perimeter of the trapezium = sum of all sides

**Parallelogram**

Area of parallelogram = base x height

Perimeter of parallelogram = 2(base+height)

## Polygonal and Non-polygonal Plane Shapes

Closed **shapes** can further be characterized into **polygonal** and non-polygonal plane shapes. A **polygon** is formed only by line segments and has at least 3 **sides**. If any side of a plane figure is not straight (curved), it is not a **polygon**.

Squares, **rectangles**, parallelograms, trapeziums, etc., are examples of polygonal plane shapes, whereas **circles**, ovals, ellipses, etc., are examples of **non-polygonal** plane shapes.

## Open Plane Shapes

Open shapes are a **combination** of line segments and **corners,** but they have at least one **opening**, i.e., any one of the **corners** is not connected to the **side**. It may be a **straight** or **curved** **line** or any other **irregular** shape that has an open face. Angles are an example of **open** shapes.

### Solid Shapes

In **mathematics**, a solid shape is a flat, closed and **3-dimensional** figure. The term 3 dimensional refers to the **fact** that these figures have **length**, width, and **height**. Cuboids, **spheres**, cylinders, and **cubes** are some examples of solid shapes.

As plane shapes refer to **2-dimensional** figures, solid **shapes** are **3-dimensional** figures. **Plane** shapes are easy to construct, whereas solid **shapes** are quite complex to **construct**.

## Solved Examples Related to Plane Shapes

### Example 1

Calculate the area and perimeter of a parallelogram whose base and height are 10m and 5m, respectively.

### Solution

Given:

base=10m

height=5m

Area =?

perimeter=?

The formula for the area and perimeter of the parallelogram is:

**Area** = base*height

A = 10m*5m

**A = 50m$^2$**

**Perimeter** = 2(base*height)

P = 2(10m*5m)

P = 2(50)

**P = 100m**

Hence, the perimeter of the parallelogram is 100m, and the area is 50m$^2$.

### Example 2

What is the circumference of a circle with a radius of 5cm?

### Solution

Given radius = 5cm

Circumference =?

To find the circumference, we use the formula

**Circumference** = 2*pie*r

C = 2*pie*5cm

**C = 31.4cm**

Hence, the circumference of the circle is 31.4cm.

*All images are created using GeoGebra. *