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1.5 Measurement




Perimeter

Perimeter is the distance around a shape.

Possible units include millimeters (mm), centimeters (cm), meters (m) and kilometers (km). The conversion relationship is as follows:

The perimeter of a circle is given by the formula C=2\pi r. For example, this circle with radius 3.8cm:

Circumference can be calculated as C=2\pi r=2\pi(3.8)=23.88cm.

Area

Possible units of areas include millimeters squared (mm^2), centimeters squared (cm^2), meters squared (m^2), kilometers squared (km^2), and hectares.

The area of a square is =l^2:

The area of a rectangle is =l*w:

The area of a circle is =\pi r^2:

The area of a triangle is =\dfrac{1}{2}bh:

The area of a parallelogram is =b*h:

The area of a trapezium is =\dfrac{1}{2}(a+b)*h:

For example, to find the area of a trapezium as enlisted:

To solve for the area of this trapezium, A=\dfrac{1}{2}(a+b)*h=\dfrac{10+5}{2}*4=7.5*4=30m^2.

Surface area

Surface area is the sum of the area of each individual face of an object.

The surface area of a sphere is =4\pi r^2

The surface area of a curved surface cylinder is =2\pi rh=(r*h)*\pi

The surface area of a curved surface of a cone is =\pi rs

Volume

The volume is the amount of space occupied by a three-dimensional object, measured in cubic units (e.g. liters or meters). It is the amount of substance occupying a particular volume.

A cubic centimeter (cm^3) looks as follows:

A cubic meter (m^3) looks as follows:

A prism is a polyhedron with two polygonal faces lying in parallel planes and with other faces parallelograms.

The most common prism is the rectangular prism (where a rectangle forms the base), of which the volume is V=l.w.h.

The triangular prism (with a triangle base), where the volume can be calculated as Volume = Area of base * Height = \dfrac{b*h}{2}*H.

The cylinder (with a circle base), where the volume can be calculated as Volume = Area of base * Height, V=\pi r^2*H.

Another prism (with again, an identical cross-section):

Capacity

Capacity is the maximum amount that can be contained/accomodated, which is:

  • 1mL=1cm^3
  • 1L=1000cm^3
  • 1kL=1m^3
  • 1ML=1000m^3

Solid shapes

The shape of a prism is:

The shape of a cube is:

The shape of a pyramid is:

Compass

A compass is a device which helps to determine directions by the means of a (or a group of) magnetic needles, which turn freely on a pivot, and point to the magnetic north.

Going clockwise, north (N) is marked on the compass at the top, to the right is east (E), downwards is south (S) and to the left is west (W). You can remember this by “Never (N), Eat (E), Soggy (S), Weetbix (W)”.

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