Perimeter and areaIB MYP Maths Extended: Revision notes

The perimeter is the total distance around the outside of a shape. The area is the amount of surface inside it, measured in square units such as cm$^2$.

• Rectangle: area $=l\times w$, perimeter $=2(l+w)$.
• Triangle: area $=\frac12\times\text{base}\times\text{perpendicular height}$. The height must be at right angles to the base. A sloping side is not the height unless the triangle is right-angled.

A parallelogram has area $=\text{base}\times\text{perpendicular height}$. A trapezium has one pair of parallel sides $a$ and $b$ and area $A=\frac12(a+b)h,$ where $h$ is the perpendicular distance between the parallel sides. Example: parallel sides $9$ cm and $15$ cm, height $6$ cm gives $\frac12(24)(6)=72$ cm$^2$. Other quadrilaterals can be split into triangles or rectangles.

For a circle of radius $r$ and diameter $d=2r$: $C=2\pi r=\pi d,\qquad A=\pi r^2.$ Use the $\pi$ button on your calculator and round only at the end. Example: $r=5$ cm gives $C=10\pi=31.4$ cm and $A=25\pi=78.5$ cm$^2$. Check whether you are given the radius or the diameter before you start.

A sector is a slice of a circle between two radii. If the angle at the centre is $\theta$, the sector is a fraction $\frac{\theta}{360}$ of the whole circle: $\text{arc length}=\frac{\theta}{360}\times2\pi r,\qquad \text{sector area}=\frac{\theta}{360}\times\pi r^2.$ Example: $r=12$ cm and $\theta=75^\circ$ gives arc $=5\pi=15.7$ cm and area $=30\pi=94.2$ cm$^2$. The perimeter of a sector is the arc plus two radii.

A compound shape is made of simple shapes joined together, or one shape with another cut out. Split it into rectangles, triangles, circles and so on, find each area and add (or subtract a hole). For the perimeter, add only the edges on the outside. Edges where shapes join are not part of the perimeter. Example: a rectangle $14$ m by $8$ m with a semicircle (diameter $8$ m) on one short side has area $112+8\pi=137$ m$^2$ and perimeter $14+14+8+4\pi=48.6$ m. Always state the units: cm and m for lengths, cm$^2$ and m$^2$ for areas.