Geometry - 2-D and 3-D Shapes

Perimeter, Surface Area, Density, Sectors, and Arx Lengths

area of a triangle

A=bh/2

area of a trapezoid

A=((b₁+b₂)/2)h

area of an isosceles trapezoid

A=((b₁+b₂)/2)h

area of a parallelogram

A=bh

area of a rectangle

A=bh

area of a rhombus

A=bh

area of a square

A=bh

area of a circle

A = π r²

What “B” represent?

base area

volume of a general prism

V=Bh

volume of a triangular prism

V=((bh₁)/2)h₂

volume of a rectangular prism

V=lwh

volume of a cylinder

V=(πr²)h

volume of a general pyramid

V=(1/3)Bh

volume of a triangular pyramid

V=(1/3)((bh₁)/2)h₂

volume of a rectangular pyramid

V=(1/3)(bh₁)h₂

volume of a cone

V=(1/3)(πr²)h

volume of a sphere

V=(4/3)πr³

circumference of a circle

C=2πr

What do you add to find the surface area of a general prism?

the area of each face

surface area of a cylinder

SA=2πrh+2πr²

What do you add to find the surface area of a general pyramid?

the area of each face

what does “l” represent, specifically in a cone?

slant height

surface area of a cone

SA=πr²+πrl

surface area of a sphere

SA=4πr²

What is the definition of population density?

the number of people divided by the geographic area

Using the units km² for area, what is the formula for population density?

D=people/km²

What is the definition of mass density?

the mass of an object divided by its volume

What is the formula of mass density (with abbreviations)?

D=m/v

What is a sector?

a portion of a circle that is enclosed by two radii and an arc

What is sector area?

a portion of a circle’s entire area

sector area formula (just expression part)

(central angle/360)πr²

What is sector arc length?

a portion of circle’s entire perimeter

sector arc length formula (just expression part)

(central angle/360)2πr

What is lateral surface area?

surface area of a prism, pyramid, cylinder or cone without the top or bottom basses

lateral surface area of a prism

LSA = total surface area - the area of both bases

lateral surface area of a pyramid

LSA=2πrh

lateral surface area of a cylinder

LSA=2πrh

lateral surface area of a cone

LSA=πrl