BLACKSTONE VALLEY REGIONAL VOCATIONAL TECHNICAL
  HIGH SCHOOL
65 Pleasant St.
Upton, MA 01568
(508)-529-7758
 
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Shapes
Let's Learn About Shapes!

The links below have information about different shapes. Look at this web page then watch the video about how shapes are important at Blackstone Valley Tech. The video has instructions for the worksheet that you will do for homework. Then we'll talk to you LIVE over the Internet about the shapes you found at home!

1. Triangles
2. Quadrilaterals
3. Circles

4. Polygons
5. Perimeter and area
6. Symmetry
7. 3D shapes
8. Nets of 3D shapes

Homework Worksheet

Shapes
1. Triangles


Equilateral triangle
  • 3 equal sides
  • 3 equal angles of 60°

Equilateral triangle

Isosceles triangle

  • 2 equal sides
  • 2 equal angles

Isosceles triangle

Scalene triangle

  • No equal sides
  • No equal angles

Scalene triangle

Right-angled triangle

  • One of its angles is a right angle (90°)

Right angled triangle

2. Quadrilaterals
Quadrilaterals have four sides. Here are some special
quadrilaterals:


Square
  • 4 equal sides
  • 4 right angles

Square

Rectangle

  • 2 pairs of equal sides
  • 4 right angles

Rectangle

Rhombus (squashed square)

  • 4 equal sides
  • Opposite sides are parallel
  • Opposite angles are equal

Rhombus

Parallelogram (squashed rectangle)

  • 2 pairs of equal sides
  • Opposite sides are parallel
  • Opposite angles are equal

Parallelogram

Trapezium

  • One pair of parallel sides of different lengths

Trapezium

Kite

  • 2 pairs of equal sides next to each other
  • No parallel sides.

Kite

3. Circles
Circle

    • The circumference is the distance all the way
      around a circle.
    • The diameter is the distance right across the middle
      of the circle.
    • The radius is the distance halfway across the circle.
      The radius is always half the length of the diameter.

4. Polygons
Polygons are shapes with many straight sides. Regular polygons
have equal angles and sides of equal length. Irregular polygons
have sides of different lengths.

  • Pentagons have 5 sides.

Rectangular pentagon and an Irregular pentagon

  • Hexagons have 6 sides.

Rectangular hexagon and an Irregular hexagon

  • Heptagons have 7 sides.

Rectangular hectagon and an Irregular hectagon

  • Octagons have 8 sides.

Rectangular octagon and an Irregular octagon

5. Perimeter and area

  • The perimeter is the distance all the way around the
    outside of a 2D shape.
  • To work out the perimeter, add up the lengths of all
    the sides.
    The perimeter of this shape is 5 + 5 + 10 + 10 = 30 centimetres
  • The area of a 2D shape is the amount of surface
    it covers.
  • The units for area are cm2 (square centimetres),
    m2 (square metres) or km2 (square kilometres).
  • To work out the area of a rectangle, multiply
    its length (the longer side) by its width
    (the shorter side).
    The area of this rectangle is 6 x 4 = 24 centimetres squared

6. Symmetry
A 2D shape is symmetrical if a line can be drawn through it so
that either side of the line looks exactly the same. The line is
called a line of symmetry.


Square
  • 4 lines of symmetry

Square

Equilateral triangle

  • 3 lines of symmetry.

Equilateral triangle

Rectangle

  • 2 lines of symmetry

Rectangle

Isosceles triangle

  • 1 line of symmetry

Isosceles triangle

Parallelogram

  • 0 lines of symmetry

Parallelogram

7. 3D shapes
3D shapes have faces (sides), edges and vertices (corners).
The exception is the sphere which has no edges or vertices.
Examples of a Cube, Cuboid, Triangular prism, Triangular based pyramid, Square based pyramid, Cone, Cylinder, Sphere

 

8. Nets of 3D shapes

  • The net of a 3D shape is what it looks like if it is opened
    out flat. A net can be folded up to make a 3D shape.
  • There may be several possible nets for one 3D shape.

Here are some examples.
Net of a cube
Net of a cube
Net of a cuboid
Net of a cuboid
Net of a square-based pyramid
Net of a square-based pyramind
Net of a tetrahedron
Net of a tetrahedron

 

Equilateral
A figure having all the sides equal
Quadrilateral
A plane figure having four sides and four angles
Polygon
A closed plane figure having many angles and sides (more than four)
Octagon
A polygon having eight angles and eight sides
Rhombus
An oblique-angled equilateral parellelogram
Heptagon
A polygon having seven angles and seven sides
Dodecagon
A polygon having twelve angles and twelve sides
Hexagon
A polygon having six angles and six sides
Nonagon
A polygon having nine angles and nine sides
Hypotenuse
The side of a right triangle opposite the right angle
Trapezoid
A quadrilateral plane figure having two parallel and two nonparallel sides
Scalene
A triangle with three unequal sides
Isosceles
A triangle with two equal sides

 

 

 

 

 

circle with center point A

A circle is a shape with all points the same distance from the center. It is named by the center. The circle to the left is called circle A since the center is at point A. If you measure the distance around a circle and divide it by the distance across the circle through the center, you will always come close to a particular value, depending upon the accuracy of your measurement. This value is approximately 3.14159265358979323846... We use the Greek letter Pi(pronounced Pi) to represent this value. The number Pigoes on forever. However, using computers, mathematicians have been able to calculate the value of Pito thousands of places.

The distance around a circle is called the circumference. The distance across a circle through the center is called the diameter. Piis the ratio of the circumference of a circle to the diameter. Thus, for any circle, if you divide the circumference by the diameter, you get a value close to Pi. This relationship is expressed in the following formula:

  [IMAGE]

C over d equals Pi

where Cis circumference and dis diameter. You can test this formula at home with a round dinner plate. If you measure the circumference and the diameter of the plate and then divide Cby d, your quotient should come close to Pi. Another way to write this formula is: C equals Pi times dwhere · means multiply. This second formula is commonly used in problems where the diameter is given and the circumference is not known (see the examples below).

[IMAGE]

The radius of a circle is the distance from the center of a circle to any point on the circle. If you place two radii end-to-end in a circle, you would have the same length as one diameter. Thus, the diameter of a circle is twice as long as the radius. This relationship is expressed in the following formula: [IMAGE], where dis the diameter and ris the radius.

Circumference, diameter and radii are measured in linear units, such as inches and centimeters. A circle has many different radii and many different diameters, each passing through the center. A real-life example of a radius is the spoke of a bicycle wheel. A 9-inch pizza is an example of a diameter: when one makes the first cut to slice a round pizza pie in half, this cut is the diameter of the pizza. So a 9-inch pizza has a 9-inch diameter. Let's look at some examples of finding the circumference of a circle. In these examples, we will use Pi= 3.14 to simplify our calculations.

  [IMAGE]


Example 1:

The radius of a circle is 2 inches. What is the diameter?

[IMAGE]

Solution:

[IMAGE]

 

d= 2 · (2 in)

 

d= 4 in

 

 

 

 

 
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This page was last updated 06/04/2008