GCSE Maths revision · Higher: geometry

Area of a triangle using sine

Higher only

The idea

The area of any triangle is $\frac{1}{2}ab\sin C$ , where $C$ is the angle between sides $a$ and $b$ .

Watch out The angle must be the one between the two sides you use.

Worked exampleCalculator allowed2 marks

The diagram shows a triangle.

Work out the area of the triangle. Give your answer correct to 3 significant figures.

Area $= \frac{1}{2}a b\sin C$ with the included angle. $\tfrac{1}{2} \times 8 \times 11 \times \sin 47^\circ = 32.18\ldots$

Answer $32.2\text{ cm}^2$

Question 1Calculator allowed2 marks

The diagram shows a triangle.

Work out the area of the triangle.

Give your answer correct to 1 decimal place.

Question 2Non-calculator3 marks

The diagram shows a sector $OAB$ of a circle with centre $O$ .

The chord $AB$ cuts off the shaded segment.

Work out the exact area of the shaded segment.

Give your answer in the form $a\pi - b\sqrt{3}$ .

Question 3Non-calculator3 marks

The diagram shows part of a circle with centre O and radius 10 cm. A and B are points on the circle.

Work out the exact area of the shaded minor segment. Give your answer in terms of $\pi$ and surds.

You must show your working.

26 official questions in 26 papers since 2017. The latest:

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