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Grade 7 · Higher · free GCSE maths worksheet

Area of a triangle using 1/2 ab sin C

Using two sides and the included angle.

14 original questions, 48 marks. Print the worksheet, mark it with the answers sheet, and use the solutions to see every step written out by hand.

Worksheet PDFWorked solutions PDFAnswers PDF

The questions

1

In triangle ABC, AB = 6 cm, AC = 9 cm and angle BAC = 40°.

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

6 cm9 cm40°ABCDiagram NOT accurately drawn
2 marks
Show answer
17.4 cm²
2

In triangle PQR, PQ = 8 cm, PR = 11 cm and angle QPR = 52°.

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

8 cm11 cm52°PQRDiagram NOT accurately drawn
2 marks
Show answer
34.7 cm²
3

ABCD is a parallelogram. AB = 12 cm, AD = 7.5 cm and angle DAB = 65°.

Calculate the area of the parallelogram. Give your answer correct to 3 significant figures.

2 marks
Show answer
81.6 cm2
4

In triangle DEF, DE = 9.4 cm, DF = 12.6 cm and angle EDF = 105°.

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

9.4 cm12.6 cm105°DEFDiagram NOT accurately drawn
2 marks
Show answer
57.2 cm²
5

In triangle ABC, AB = 9 cm and AC = 8 cm.

The area of the triangle is 30 cm2.

Angle BAC is acute.

Work out the size of angle BAC. Give your answer correct to 1 decimal place.

9 cm8 cmABCDiagram NOT accurately drawn
3 marks
Show answer
56.4°
6

In triangle PQR, PQ = 10 cm and PR = 12 cm.

The area of the triangle is 45 cm2.

Angle QPR is obtuse.

Work out the size of angle QPR. Give your answer correct to 1 decimal place.

3 marks
Show answer
131.4
7

In triangle XYZ, XY = 10 cm and angle YXZ = 35°.

The area of the triangle is 42 cm2.

Work out the length of XZ. Give your answer correct to 3 significant figures.

10 cm35°XYZDiagram NOT accurately drawn
3 marks
Show answer
14.6 cm
8

In triangle ABC, AB = 8 cm, BC = 12 cm and AC = 15 cm.

  1. Work out the size of angle ABC. Give your answer correct to 1 decimal place.
  2. Work out the area of the triangle. Give your answer correct to 3 significant figures.
8 cm12 cm15 cmABCDiagram NOT accurately drawn
5 marks
Show answer
a) 95.1° b) 47.8 cm²
9

A rectangle measures 9 cm by 4 cm.

A triangle has two sides of length 10 cm and 12 cm, with an acute angle of x° between them.

The area of the triangle is equal to the area of the rectangle.

Work out the value of x. Give your answer correct to 1 decimal place.

4 marks
Show answer
36.9
10

A and B are points on a circle with centre O.

The circumference of the circle is 40 cm.

Angle AOB = 68°.

Calculate the area of triangle AOB. Give your answer correct to 3 significant figures.

68°OABDiagram NOT accurately drawn
4 marks
Show answer
18.8 cm²
11

A and B are points on a circle with centre O and radius 10 cm. Angle AOB = 80°.

The chord AB cuts off a segment of the circle (the region between the chord AB and the minor arc AB).

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

4 marks
Show answer
20.6 cm2
12

ABCDE is a regular pentagon with sides of length 9 cm.

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

ABCDE9 cm9 cmDiagram NOT accurately drawn
4 marks
Show answer
38.5 cm²
13

In triangle ABC, AB = 16 cm, angle BAC = 54° and angle ABC = 71°.

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

16 cm54°71°ABCDiagram NOT accurately drawn
5 marks
Show answer
120 cm²
14

ABCD is a quadrilateral. The diagonal BD splits it into two triangles.

In triangle ABD, AB = 9 cm, BD = 13 cm and angle ABD = 42°.

In triangle BCD, BC = 11 cm and angle DBC = 51°.

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

9 cm11 cm13 cm42°51°ABCDDiagram NOT accurately drawn
5 marks
Show answer
94.7 cm²

Every question here is original and written by Robinson Tuition. The grade follows the Edexcel grade descriptors and suits AQA and OCR too; this is not an exam-board paper.

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