IGCSE Mathematics 0580

Geometry: Mensuration

This section covers the calculation of perimeter, area, surface area, and volume of two-dimensional and three-dimensional shapes.

1. Perimeter

Perimeter is the total distance around the outside of a shape.

• Square: $P = 4s$ (where $s$ is the side length)
• Rectangle: $P = 2(l + w)$ (where $l$ is length and $w$ is width)
• Triangle: $P = a + b + c$ (where $a$, $b$, and $c$ are the lengths of the sides)
• Circle: $P = 2\pi r = \pi d$ (where $r$ is the radius and $d$ is the diameter)

2. Area

Area is the amount of surface a two-dimensional shape covers.

• Square: $A = s^2$
• Rectangle: $A = l \times w$
• Triangle: $A = \frac{1}{2} \times base \times height = \frac{1}{2}bh$
• Circle: $A = \pi r^2$

3. Surface Area

Surface area is the total area of all the surfaces of a three-dimensional shape.

Shape	Formula
Cube:	$SA = 6s^2$ (where $s$ is the side length)
Cuboid:	$SA = 2(lw + lh + wh)$ (where $l$ is length, $w$ is width, and $h$ is height)
Cylinder:	$SA = 2\pi r^2 + 2\pi rh = 2\pi r(r + h)$ (where $r$ is radius and $h$ is height)
Sphere:	$SA = 4\pi r^2$ (where $r$ is the radius)

4. Volume

Volume is the amount of space a three-dimensional shape occupies.

Shape	Formula
Cube:	$V = s^3$ (where $s$ is the side length)
Cuboid:	$V = l \times w \times h$ (where $l$ is length, $w$ is width, and $h$ is height)
Cylinder:	$V = \pi r^2 h$ (where $r$ is radius and $h$ is height)
Sphere:	$V = \frac{4}{3}\pi r^3$ (where $r$ is the radius)

Suggested diagram: A square with side length 's' labeled, a rectangle with length 'l' and width 'w' labeled, a triangle with sides 'a', 'b', and 'c' labeled, a circle with radius 'r' labeled, a cube with side length 's' labeled, a cuboid with length 'l', width 'w', and height 'h' labeled, a cylinder with radius 'r' and height 'h' labeled, and a sphere with radius 'r' labeled.