Shapes in Geometry and Their Measurements

Geometry

In Mathematics, geometry is one of the crucial branches that help us to understand the shapes and sizes of the object we see in our day to day life. The basic of shapes starts with points, lines and angles. Point is simply a dot or a node, where two lines are joined together. Whereas an angle is formed when two lines are connected to each other, end to end.

Points and lines are one dimensional. But we usually learn the geometrical shapes and their measurements based on two-dimensions and three-dimensions. These shapes have various applications in different fields such as Constructions, Architecture, Engineering, Interior Designing, Graphic designing, Gaming, etc.

For example, we use these to determine the area of floor in a building, length of a pole in a street, length of boundaries of a plot to fence it, etc.. And also, for domestic purposes such as cylinder area will determine the surface area of a cylindrical shape in a 3d space, a circle drawn on a ground of a specific diameter to dig a hole, etc. So, geometry has many applications in various fields. Let us learn here different shapes and their measurements based on the dimensions.

Two-Dimensional Shapes in Geometry

The two-dimensional shapes in geometry are circle, triangle, quadrilaterals and all the polygons that have area and perimeter. These are defined in the XY plane, along x-axis and y-axis. All the closed curves and polygons are two-dimensional. Let us discuss all the 2d shapes here.

Circle

A circle is a closed curve shape that has locus of points at an equidistant from a common point, called center. The distance from center to the locus of points or outer line of circle, is called the radius. Area and circumference of circle is given by:

Area (sq.unit) Pi (Radius)2
Circumference (units) 2 Pi (Radius)

Triangle

A triangle is a three sided closed shape, where each side is connected to two other sides end to end. It is the smallest kind of polygon having three sides and three interior angles.

Area  (sq.unit) ½ (Base) x (Height)
Perimeter (units) a+b+c; sum of three sides

Quadrilateral

A four sided closed shape, that has four interior angles. It is also categorised into different types:

  • Square: All sides are equal and all angles are equal to 90 degrees
  • Rectangle: Opposite sides are equal and all angles measures 90 degrees
  • Parallelogram: Opposite sides are equal and parallel. Opposite angles are equal.
  • Trapezium: One pair of opposite sides are parallel.
Type of quadrilateral Area (sq.unit) Perimeter (units)
Square Side2 4 x Side
Rectangle Length x Width 2 (Length + Width)
Parallelogram Base x Height 2 (Sum of any two adjacent sides)
Trapezium ½ (sum of parallel sides) x (height) Sum of all sides

Three-Dimensional Shapes

Three dimensional shapes are those shapes that are defined in three dimensions such as x-axis, y-axis and z-axis. The additional z-axis here represents the thickness of the shape. The basic solid shapes in Maths are:

Why Learn Geometry? Definition and Uses

  • Sphere
  • Cube
  • Cuboid
  • Cone
  • Cylinder

These solid shapes are defined based on their surface area and volume. Let us learn the measurement of these solids.

Sphere

A sphere is a round shape whose surface is at equidistant from a common point, called center. Similar to circle, the distance from center to outer surface is the radius of the sphere.

Surface area 4πr² (square unit)
Volume 4/3(πr3)  (cubic unit)

Cube

A cube is an extended version of a square in three dimensional space, whose all the sides are of square shape. Therefore, the length of all its edges are also equal. It has 6 faces, 12 edges and 8 vertices.

Surface area 6 (Edge)2 (square unit)
Volume Edge3 (cubic unit)

Cuboid

A cuboid is an extended version of a rectangle. Just like a cube, it also has 6 faces, 12 edges and 8 vertices. But the faces of cuboids are in rectangular shape.

Surface area 2 (Length x Breadth+breadth x height + Length x height)
Volume length × breadth × height

Cone

A cone is a solid shape with a circular base, that narrows smoothly from bottom to top at a point called the apex of the cone.

Surface area (sq.units) Πr (r+l), where r is the radius of circular base and l is the slant height
Volume (cu.units)  ⅓ Π (r2) (h); h is the height of cone

Cylinder

Cylinder is a 3d shape having parallel circular bases on both the sides of a curved surface.

Surface  area (sq.units) 2 Π r (r + h); r and h are the radius and height of cylinder
Volume (cu. units) Π r2 h

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