Measurement: Length, Area, and Volume

Area and Perimeter

Polygons

Area

r

The area is the size of a surface within a perimeter.

a

Rectangles

r

Area of a Rectangle = Length times WidthA = lw

Parallelograms

r

Area of a Parallelogram = Base times HeightA = bh

Trapezoids

r

Area of a Trapezoid = 1/2 (Base a + Base b) x HeightA = 1/2 (a + b)h

a

Triangles

r

To find the the area if a triangle you will multiply the base by the height and then divide by 2 (since a triangle is half of a parallelogram)Area of a Triangle = 1/2 x Base x Height or Base x Height / 2A = 1/2bh or A = bh / 2

Perimeter

r

The perimeter is the distance around a shape.You will add the lenghs of all sides together.

a

Circles

r

The perimeter of a circle is called circumference.The diameter is the distance across a circle throuht the center.The radius of a circle is the distance form the center of a circle. The ratio of a circle's circumference to its diameter is called Pi. Pi = 3.14159.

Area

r

Area of a Circle = Pi times the Radius squaredA = Pi x r x r

Perimeter

r

Circumference = 2 times Pi times radiusC = 2 x Pi x r

Irregular shapes

Surface Area

r

Surface area measures total area of the surface of a three dimensional shape.

a

Prisms

r

Surface area of prismsSA = 2B + phB = area of base p = perimeter of the baseh= height

Cylinders

r

Surface area of cylindersSA = 2B + phB = area of base p = perimeter of the baseh= height

Pyramids

r

Surface area of pyramidsSA = B + 1/2ps

Cones

r

Surface area of conesSA = Pi r squared + Pi rs

Spheres

r

Surface area of a sphereS = 4Pi r squared

The Measurement Process

The U.S. Customary System

Units of Length, Capacity and Weight

Units of Area

Units of Volume

Temperature - Fahrenheit

r

F boiling point minus F freezing point divided by C boiling point minus C freezing point212 - 32 / 100 - 0 = 1.8 or 9/5 Fahrenheit to CelsiusC = 5/9 (F-32)

a

The International System (Metirc Units)

Metric Units of Length, Capacity and Mass

a

Metric Units of Area

Temperature - Celsius

r

F boiling point minus F freezing point divided by C boiling point minus C freezing point212 - 32 / 100 - 0 = 1.8 or 9/5 Celsius to FahrenheitF = 1.8C + 32

Volume

r

Volume is the measure of the amount of space that is inside of a three dimensional shape.

Prisms

r

Volume = length x width x heightV = lwh

Cylinders

r

Volume of a Cylinder is base x heightV = Bh

Pyramids

r

Volume of a Pyramid V = 1/3Bh

Cones

r

Volume of a coneV = 1/3Bh

Spheres

r

Volume of a SphereV = 4/3 Pi r3