This document provides formulas for calculating geometric properties of various 2D and 3D shapes. It includes formulas for calculating the perimeter and area of rectangles, squares, triangles, and circles. It also provides formulas for calculating the surface area and volume of 3D shapes like rectangular prisms, triangular prisms, cylinders, cones, spheres, and square-based pyramids.

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