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Trigonometry · Guided Practice

Triangle Area

11 questions with answers and video solutions. Try each one before revealing the answer.

1
In the triangle below, BC = 9 mm, AC = 15 mm and angle C = 60°.

Triangle ABC with side lengths and angle

Calculate the area of triangle ABC.

2
In the triangle below, AB = 5 cm, BC = 3 cm and sin B = 12.\displaystyle \frac{1}{\sqrt{2}} .

Triangle ABC with side lengths and sine of angle B

Calculate the area of triangle ABC, expressing your answer as a fully simplified surd with a rational denominator.

3
Calculate the area of an equilateral triangle with side lengths of 5 cm.
4
Calculate the area of a regular hexagon with side length 10 cm, giving your answer correct to 3 significant figures.
5
A triangle of area 50 cm2 has two sides with lengths 12 cm and 10 cm. The angle between these two sides is acute.
Calculate this angle.
6
A triangle of area 50 cm2 has two sides with lengths 12 cm and 10 cm. The angle between these two sides is obtuse
Calculate this angle.
7
2015 P2 Q11
4 Marks

The top of a table is in the shape of a regular hexagon. The three diagonals of the hexagon which are shown as dotted lines in the diagram below each have length 40 centimetres.

Regular hexagon with diagonals

Calculate the area of the top of the table.

8
2017 P1 Q7
2 Marks

In triangle DEF:
DE = 8 cm, EF = 12 cm, sin⁡E=23.\displaystyle \sin E = \frac{2}{3}.

Triangle DEF

Calculate the area of triangle DEF.

9
2019 P2 Q3
2 Marks

The diagram shows triangle PQR.

Triangle PQR

•  PR = 45 centimetres
•  PQ = 70 centimetres
•  Angle QPR = 129°
Calculate the area of triangle PQR.

10
2023 P2 Q15
4 Marks

In the diagram:
•  AC is perpendicular to BC
•  AB = 18 centimetres
•  BD = 6 centimetres
•  BC = 8 centimetres.

Triangle ADE with perpendicular AC to BC

The area of triangle ADE is 160 square centimetres.
Calculate the length of AE.

11
2025 P1 Q5
2 Marks

Triangle ABC is shown in the diagram.

Triangle ABC

• AB = BC = 6 centimetres.
∙sin⁡B=23.\displaystyle \bullet \quad \sin B = \frac{2}{3}.
Calculate the area of the triangle.

Practice questions courtesy of Maths.scot. Full written solutions are on his site — the links above go straight to them.

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