L

W

L

W

L

L

L

L

c

b

a

b

h h

b

d

LW

H

Beaconhouse School System SBGR

2D –geometric shape: square, rectangle, triangle, circle, trapezoid, parallelogram, etc.

Composite figure: a combination of 2 or more geometric shapes e.g. e.g.

3D –geometric shape: rectangular prism, triangular prism, cylinder, cone, sphere, pyramid, etc.

Calculate the Perimeter of a Rectangle: distance around the rectangle (add up the lengths of all 4 sides)

P = L + L + W + W or P = 2L + 2W or P = 2(L + W)

Calculate the Area of a Rectangle: number of square units that it covers (multiply length x width)

A = L x W

Calculate the Perimeter of a Square: distance around the square (add up length of all 4 sides)

P = L + L + L + L or P = 4L

Calculate the Area of a Square: number of square units that it covers (multiply length x length)

A = L x L or A = L2

Calculate the Perimeter of a Triangle: distance around the triangle (add up the lengths of all 3 sides)

P = a + b + c

Calculate the Area of a Triangle: number of square units that it covers ( ½ x base of triangle x height of triangle)

A =

base x height2 A =

b h2

Calculate the Circumference of a Circle: distance around the circle (the “perimeter” of the circle)

C = 2π r or C = π d (r is radius) (d is diameter)

Calculate the Area of a Circle: number of square units that it covers (π x radius x radius)

A = π r2 A = π x r x r

Calculate the Surface Area of a Rectangular Prism: add up the areas of all 6 sides of the prism SA = (2 x L x W) + (2 x L x H) + (2 x W x H)

Or SA = 2(LW + LH + WH)

Calculate the Volume of a Rectangular Prism: amount of space it takes up (area of base x height of prism)

V = area of the rectangle base x height of the prism V = L x W x H

r

LW

H

Beaconhouse School System SBGR

r

r

bb

s

bb

h

Beaconhouse School System SBGR

Calculate the Surface Area of a Triangular Prism: add up the area of all 5 sides (2 triangles, 3 rectangles) of the prism

SA =

base x height2 +

base x height2 + LW + LW + LW

SA = area triangle + area triangle + area rectangle + area rectangle + area rectangle

Calculate the Volume of a Triangular Prism: amount of space it takes up (area of base triangle x height of prism)

V = area of base triangle x height of prism

V =

base x height2 x height of prism V =

bh2 x h of prism

Calculate the Surface Area of a Cylinder: area of the 2 circles and the area of the rectangle

SA = 2π r2 + 2π r x height of cylinder SA = ( area of 2 circles 2π r2 ) + ( area of rectangle 2π r x h )

Calculate the Volume of a Cylinder: amount of space it takes up

V = π r2 x h V = (area of the base circle π r2 ) x ( height of the cylinder h )

Calculate the Volume of a Cone: amount of space it takes up

V =

13π

r2 x h OR V =

πr2 h3

V = (1/3) x (area of the base circle) x (height of the cone)

Calculate the Surface Area of a Sphere: amount of space it takes up

SA = 4π r2

SA = 4 x area of the circle cross-section (π r2) at the equator of the sphere

Calculate the Volume of a Sphere: amount of space it takes up

V =

43πr3

Calculate the Surface Area of a Square-Based Pyramid: area of all the faces (square base, and 4 triangles)

SA = b2 + 4(

b h2 ) where s = (slant) height of a triangular face

SA = (area of the square base + areas of 4 side triangles)

Calculate the Volume of a Square-Based Pyramid: amount of space it takes up

V =

13b2h

V = one-third the area of the square base (b2) x height of the pyramid (h)

height of prismh

b

h

h

r

h

r

r