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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

Find the mass of the annulus and 3D object

1) (From prob_4.doc) Find the mass of the annulus (donut shape) having radius 1<r<2 when the density funciton rho(r,theta) = (1-ar^2) where a is a constant. 2) (From prob_5.doc) Find the total mass of the 3D object when the mass density rho and the object size is rho(r,phi,theta)=r^2sin(theta) where 1<r<2, 0<phi<pi and 0<thet

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.

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

Finding Angles

The distance from A to B is 4 metres. The angles shown are in degrees. What is the angle of alpha?

Finding the Lengths and Angles of Arcs

Question#1 Two streets meet at an angle of 83.0 degrees. What is the length of the piece of curved curbing at the intersection if it is constructed along the arc of a circle 15.0 ft in radius? Question #2 Through what angle does the drum turn in order to lower the crate 18.5 feet. The drum has a circumference of 2.38 feet

Similar Shapes : Volume, Height, Circumference and Area

Please complete the attached and explain steps or formulas: 12 their volumes 15 their volumes 20. Two similar cylinders have bases with areas 16 cm sq. 2 and 49 cm sq. 2 . If the larger cylinder has height 21 cm, find the height of the smaller cylinder. 22. their volumes 23. the areas of their bases 25. their volumes 26.

Vectors : Work, Scalar Projection and Diagonal of a Cube

46. Find the work done by a force of 20 lb acting in the direction N50°W in moving an object 4 ft due west. 49. Use a scalar projection to show that the distance from a point P1(x1, y) to the line ax + by + c = 0 is... Use this formula to find the distance from the point (?2, 3) to the line 3x ? 4y + 5 = 0. 50. Find the angl

Equation of a Sphere: Three-dimensional space

14. Find an equation of the sphere that passes through the origin and whose center is (1, 2, 3). 19. (a) Prove that the midpoint of the line segment from P1(x1, y1, z1) to P2(x2, y2, z2) is (((x1 + x2)/2), ((y1 + y2)/2), ((z1 + z2)/2)) (b) Find the lengths of the medians of the triangle with vertices A(1, 2, 3), B(-2, 0

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...


A right triangle has one angle that measures 90 degree. If one of the acute angles is 2 times the size of the other, what is the measure of the smallest angle? Explain your answer. The cake recipe calls for 14 ounces of cream cheese. How much of the cream cheese will be left over? Show your answer in pounds and ounces.

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?

Find the radius of a circle and find lengths of arcs

1.If an arc 70mm long subtends an angle of pi over 4 radians at the centre what is the radius of the circle? 2.A chord of length 26mm is drawn in a circle of 35mm diameter. What are the lengths of the smaller and larger arcs into which the circumference is divided?

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.

Determining the Congruence of Segments

Use the information below to answer the question: Is the segment PB congruent to PD? Segment PA is orthogonal to the plane m Points A,B,C,and D lie in the plane m Segment AB is congruent to the segment AD