\frac12\timesbase\timesperpendicular height

Area of a sector with angle \theta?

\frac{\theta}{360}\times\pi r^2

How do you find the area of a compound shape?

Split it into simple shapes, find each area, then add (or subtract a hole).

Which edges count in the perimeter of a compound shape?

Only the outside edges, not the edges where shapes join.

Square units, such as cm^2 and m^2.

Perimeter and areaIB MYP Maths Extended: Flashcards

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Area of a triangle?

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Area of a triangle?: $\frac12\times\text{base}\times\text{perpendicular height}$
Area of a parallelogram?: $\text{base}\times\text{perpendicular height}$
Area of a trapezium?: $\frac12(a+b)h$
Circumference of a circle?: $C=2\pi r=\pi d$
Area of a circle?: $A=\pi r^2$
Arc length of a sector with angle $\theta$ ?: $\frac{\theta}{360}\times2\pi r$
Area of a sector with angle $\theta$ ?: $\frac{\theta}{360}\times\pi r^2$
Perimeter of a sector?: Arc length $+\,2r$
Perimeter of a rectangle?: $2(l+w)$
How do you find the area of a compound shape?: Split it into simple shapes, find each area, then add (or subtract a hole).
Which edges count in the perimeter of a compound shape?: Only the outside edges, not the edges where shapes join.
Units for area?: Square units, such as cm $^2$ and m $^2$ .

Exam questions on Perimeter and area

A sector $OAB$ of a circle has centre $O$ , radius $12$ cm and angle $AOB=75^\circ$ . Use the $\pi$ button on your calculator.
Find the perimeter of the sector.2 marks
A trapezium has parallel sides of length $9$ cm and $15$ cm. The perpendicular distance between the parallel sides is $6$ cm.
A triangle has a base of $15$ cm and the same area as the trapezium. Find its perpendicular height.2 marks
A window is made from a rectangle $1.2$ m wide and $1.5$ m high, with an isosceles triangle on top. The triangle has a base of $1.2$ m, a perpendicular height of $0.5$ m, and each of its sloping sides is $0.78$ m long.
Find the total area of the window.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).