Mathematics-742(Things to know)

Mathematics:

Geometry

NameSidesAngles
Triangle33
Quadrilateral44
Pentagon55
Hexagon66
Heptagon77
Octagon88
Nonagon99
Decagon1010

How to find the area of a square:

  • The area of a square can be found by multiplying the base times itself. This is similar to the area of a rectangle but the base is the same length as the height.
  • If a square has a base of length 6 inches its area is 6*6=36 square inches

How to find the area of a rectangle:

  • The area of a rectangle can be found by multiplying the base times the height.
  • If a rectangle has a base of length 6 inches and a height of 4 inches, its area is 6*4=24 square inches

    How to find the area of a parallelogram:

    • The area of a parallelogram can be found by multiplying the base times the height.
    • If a parallelogram has a base of length 6 inches and a height of 4 inches, its area is 6*4=24 square inches

A trapezoid is a quadrilateral (has 4 sides) and has only one pair of sides parallel.

How to determine the area of a trapezoid:

  • Add the lengths of the 2 parallel sides
  • divide by 2 to get the average length of the parallel sides.
  • Multiply this by the height (distance between the parallel sides

How to find the area of a triangle:

  • The area of a triangle can be found by multiplying the base times the one-half the height.
  • If a triangle has a base of length 6 inches and a height of 4 inches, its area is 6*2=12 square inches

How to find the area of a circle:

  • The area of a circle can be found by multiplying pi ( π = 3.14) by the square of the radius
  • If a circle has a radius of 4, its area is 3.14*4*4=50.24
  • If you know the diameter, the radius is 1/2 as large

The perimeter of a square is the distance around the outside of the square. A square has four sides of equal length. The formula for finding the perimeter of a square is 4*(Length of a Side).

The perimeter of a rectangle is the distance around the outside of the rectangle. A rectangle has four sides with opposite sides being congruent. The formula for finding the perimeter is Side A + Side B + Side A + Side B. This could also be stated as 2*Side A + 2*Side B or 2*(Side A + Side B)

The circumference of a circle is the distance around the outside of the circle. It could be called the perimeter of the circle.

How to find the circumference of a circle:

  • The circumference of a circle can be found by multiplying pi ( π = 3.14 ) by the diameter of the circle.
  • If a circle has a diameter of 4, its circumference is 3.14*4=12.56
  • If you know the radius, the diameter is twice as large.

To calculate the surface are of a cube, find the surface area of one side and multiply by 6. The surface area of any side is the length of a side squared.

Example: Surface area of a cube with a side of length 4 = 4*4*6 = 96

 

A rectangular prism has 2 ends and 4 sides. Opposite sides have the same area. The surface area is the sum of the areas of all six sides.

How to find the surface area of Rectangular Prisms:

  • Find the area of two sides (Length*Height)*2 sides
  • Find the area of adjacent sides (Width*Height)*2 sides
  • Find the area of ends (Length*Width)*2 ends
  • Add the three areas together to find the surface area
  • Example: The surface area of a rectangular prism 5 cm long, 3 cm. wide and 2 cm. high = 5*2*2 + 3*2*2 + 5*3*2 = 20 + 12 + 30 = 62 cm2.

To find the surface area of a cylinder add the surface area of each end plus the surface area of the side. The surface area of each end is the p r2. There are two ends so their combinded surface area is 2 p r2. The surface area of the side is the circumference times the height or 2 p r h

The entire formula for the surface area of a cylinder is

 2 π r2 + 2 π r h

The volume of a cube is (length of side)3.

The volume of a rectangular prism can be found by the formula:
volume=length*width*height

The volume of a triangular prism can be found by the formula:

volume=1/2*length*width*height

The volume of a cylinder equals the (area of the base)*height = π r2 h