1. 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 = L
2
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 =
2
heightxbase
A =
2
hb
Calculate the Circumference of a Circle: distance around the circle (the “perimeter” of the circle)
C = 2 r or C = d
(r is radius) (d is diameter)
Calculate the Area of a Circle: number of square units that it covers ( x radius x radius)
A = r
2
A = 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
c
b
a
r d
L
W
H
L
W
H
b
h h
b
L
W
L
W
L
L
L
L

2. 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 =
2
heightxbase
+
2
heightxbase
+ 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 =
2
heightxbase
x height of prism V =
2
bh
x h of prism
Calculate the Surface Area of a Cylinder: area of the 2 circles and the area of the rectangle
SA = 2 r
2
+ 2 r x height of cylinder
SA = ( area of 2 circles 2 r
2
) + ( area of rectangle 2 r x h )
Calculate the Volume of a Cylinder: amount of space it takes up
V = r
2
x h
V = (area of the base circle r
2
) x ( height of the cylinder h )
Calculate the Volume of a Cone: amount of space it takes up
V =
3
1
r
2
x h OR V =
3
hr2
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 = 4 r
2
SA = 4 x area of the circle cross-section ( r
2
) at the equator of the sphere
Calculate the Volume of a Sphere: amount of space it takes up
V = 3
r
3
4
Calculate the Surface Area of a Square-Based Pyramid: area of all the faces (square base, and 4 triangles)
SA = b
2
+ 4(
2
hb
) 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 = hb
3
1 2
V = one-third the area of the square base (b
2
) x height of the pyramid (h)
height of prism
h
b
r
h
r
h
r
h
r
r
b
b
s
b
b
h