Area-volume flashcards

Scale factor for similar shapes

a:b —- a² : b² ——— a³:b³

apothem

Line that goes from the center of polygon to the midpoint of a side

radius

line from center of polygon to vertex

Interior Angles of a Polygon (equation)

(n-2) x 180

equation for exterior angles of a polygon

360/n

30-60-90 triangle

short side - x, medium side - (x)(root 3), Hypotenuse - 2x

45-45-90 triangle

two equal sides - x, hypotenuse - (x) (root 2)

Circumference of circle

2 x pi x r

Area of circle

pi x r²

Regular Pyramid definition

• base is a regular polygon

• all lateral faces (sides) are congruent isosceles triangles. The slant height of a regular pyramid is the height of the triangular lateral face (side) 

• the altitude intersects the base at its center

Right pyramid (definition)

regular pyramid (apex is directly above center of base)

oblique pyramid

tilted (apex is not directly above center of base)

altitude of pyramid

height

slant height

distance on lateral face from apex to base edge

lateral faces

sides of pyramid

lateral edge

segment from apex to base vertex

Volume of any prism

(base area) (height)

volume of pyramid

(1/3) (base area) (height)

right cylinder

stands straight up

volume of cylinder

pi x r² x h

Volume of cone

1/3 x pi x r² x h

Volume of sphere

4/3 x pi x r³

surface area of cone

(pi x r x l) + (pi x r²)

surface area of sphere

4 x pi x r²

Surface Area of Cylinder

(2 x pi x r²) + (2 x pi x r x h)