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Geometric Shapes

Geometric shapes are figures which can be described using mathematical data, such as equations, and are an important component to the study of geometry. Basically, geometric shapes are the spatial representation of mathematical information and are unrelated to other descriptive data such as location.

The term polygon is used when describing figures which are closed and constructed of lines and points. Polygons are referred to as plane figures because they exist in two dimensions.

There are various different types of polygons and they differ in terms of their number of sides. Squares, triangles and hexagons are all examples of polygons. Additionally, other shapes such as circles which are formed by curves are also polygons. A curve is a geometric shape, but not a polygon because it is not a closed figure. Rather it is used to create polygons such as a circle or an ellipse.

In the study of geometry, analyzing the different properties of geometric shapes is a common practice. All geometric shapes differ in terms of their side lengths, number of vertices and angle measurements, to name a few features. Furthermore, the mathematical principles and theories which relate with different shapes vary and thus, having a broad understanding of geometric shapes is useful. 

Categories within Geometric Shapes


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A curve is representative of a line which is not straight.


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A circle is a basic shape used in geometry which is representative of a closed curve creating two regions which separate a plane.


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A triangle is a basic polygon used in geometry which consists of three straight lines and three angles.

The Volume of Prisms and Pyramids

1. A triangular pyramid with a base length of 9 inches, a base height of 10 inches, and a height of 32 inches. Find the volume of the figure described. 2. A square pyramid with a base length of 4 cm and a height of 6 cm resting on top of a 4 cm cube. Find the volume of the figure described. 3. The square pyramid at

Number of colored hexagons up to cyclic symmetry

If C6 acts on a regular hexagon by rotation and each of the vertices is colored red, blue or green, use the Burnsideââ?¬â?¢s formula to determine how many possible colorings there are up to cyclic symmetry.

Various problems

1. A plate glass window measures 5 ft by 8 ft. If glass costs $6 per square foot, how much will it cost to replace the window? A) $78 B) $1,440 C) $240 D) $480 2. A bedroom is 10 ft by 11 ft. What is its perimeter? A) 21 ft B) 110 ft C) 42 ft D) 55 ft 3. Turner agrees to buy a boat for $2,800 down and $129 a month

Speed, Position and Arc Length

Two identical bugs start moving at the same time on a flat table, each at the same constant speed of 20 cm/min. Assume that initially (i.e. at time t = 0) bug 1 is located at point (1, 1) and bug 2 is located at the point (-1, 1). Assume that units in the xy-plane are measured in meters and time is measured in minutes. Further

Volume of a Pipeline

The attached document shows a pipeline of 24 inch diameter (approx. 600mm) buried 1 m below the ground. There is a water pipe which prevents the pipe from going horizontally and hence it has to follow one of two pathways ie. either along the dark blue 5 mm diameter curves and exit at the bottom or along the dotted red double 40

Triangluar Array

The positive integers are written in a triangular array as shown. in what row is the number 1000? 1 23 456 78910 11...

Dimensions of a Courtyard and Perimeter of a C-shaped Building

Three buildings are connected together as one. One section is 9'2", another is 45'8" x 16'3" and the last one is 18'9" x 15'8". (The shape is a backward square letter c). What are the dimensions of the courtyard and what is the perimeter of the building?

Equation of a Frustum-Shaped Plate

What is/are the equation/s required to calculate dimensions and construction of a frustum shaped plate in its flat form before rolling into cone shape?

Inscribing a regular polygon

A clock maker wishes to make a 24 hour clock by inscribing a regular 24-gon in a circle. Determine the measure of a central angle and the measure of a vertex angle of the polygon.