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Mathematics Theorems and Formulas of Grade Five and Six
Perimeter formula: rectangle perimeter = (length+width) ×2.

C=2(a+b)

Square perimeter = side length ×4

C=4a

Circumference = π× diameter

C=πd

C

=2πr

The circumference of a semicircle = half of the circumference+diameter.

πr+d

Area formula: rectangular area = length × width.

S=ab

Square area = side length × side length

S=a2

Parallelogram area = base × height

S = ah

Triangle area = base × height ÷2

S=ah÷2

Trapezoidal area = (upper bottom+lower bottom) × height ÷2

S=(a+b)h÷2

Area of circle = π× square of radius

S=πr2

Transverse area of cylinder = bottom circumference × height.

S=Ch

Surface area formula: cuboid surface area = (length× width+length× height+width× height) ×2.

S=(ab+ah+bh)×2

Surface area of cube = side length × side length ×6

S=6a2

Side area of cylinder = bottom circumference x height.

S=C

h

Surface area of cylinder = side area+bottom area ×2

S=S side +2

The bottom of

Volume formula: cuboid volume = length× width× height.

V=abh

Cubic volume = side length × side length × side length

V=a3

Cylinder volume = bottom area × height

V=Sh

(Flatten the approximate cuboid to get: cylinder volume = half of lateral area × radius.

v = ch \2×r = 2πr \2×r =πr×r)

Cone volume = bottom area × height ÷3

V=Sh÷3 or 1/3Sh.

Relationship:

Fraction application problem

Quantity of unit "1" × fraction (percentage) = corresponding quantity.

Known quantity ÷ corresponding score (percentage) = quantity in "1"

Comparison Quantity ÷ Quantity in "1" = score (percentage)

Engineering problems:

Work efficiency × working hours = total workload.

Total workload ÷ working time = working efficiency

Total amount of work ÷ work efficiency = working hours

Encountered problems:

Speed sum × meeting time = distance

Sum of distance/speed = meeting time

Distance ÷ Meeting time = speed and

Standardization issues:

Single quantity × quantity = total quantity

Total ÷ single quantity = quantity

Total Quantity ÷ Quantity = Single Quantity

Proportion:

Distance on the map: actual distance = scale

Map distance = actual distance × scale

Actual distance = distance on map/scale.

Average value:

Total number ÷ Total number of copies = average value

y

direct proportion

——

=k

(affirmative)

Inverse ratio: xy=k (certain)

x