The smart way to improve grades

Comprehensive & curriculum aligned

Affordable pricing from £10/month

Area of a Triangle Using Trigonometry

In this worksheet, students use the trigonometrical formula to calculate the area of a triangle.

'Area of a Triangle Using Trigonometry' worksheet

Key stage:  KS 4

Curriculum topic:  Geometry and Measures

Curriculum subtopic:  Apply Pythagoras' Theorem and Trigonometric Ratios to Find Angles and Lengths in 2D Figures

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

Look at the following triangle and notice how it is conventionally labelled with the side of length a opposite the angle at A, the side of length b opposite the angle at B, and the side of length c opposite the angle at C.

The formulae for its area are:

 

Area = ½absinC

Area = ½acsinB

Area = ½bcsinA

 

Choose the most appropriate formula, depending on the information that you have.  You are looking for the given lengths of two sides and the angle between them.

 

Example

In the triangle above,

b = 4.3 cm

c = 5.1 cm

A = 38º

Use a trigonometrical formula, to calculate its area to 3 s.f.

 

Answer

Using the given information, we can only use the formula Area = ½ bcsinA.

Area = ½ x 4.3 x 5.1 x sin38º

Area = 0.5 x 4.3 x 5.1 x 0.616 = 6.7507... ≈ 6.75 cm2 (3 s.f.)

In △ABC above,

 

b = 4 cm

c = 5 cm

A = 40º

 

Use a trigonometrical formula, to calculate its area in cm2 to 3 s.f.

 

(Just write the number)

In △ABC above,

 

a = 4 cm

b = 6 cm

C = 55º

 

Use a trigonometrical formula, to calculate its area in cm2 to 3 s.f.

 

(Just write the number)

In △ABC above,

 

a = 4.5 cm

c = 6 cm

B = 85º

 

Use a trigonometrical formula, to calculate its area in cm2 to 3 s.f.

 

(Just write the number)

In △ABC above,

 

a = 6.2 cm

b = 7 cm

C = 125º

 

Use a trigonometrical formula, to calculate its area in cm2 to 3 s.f.

 

(Just write the number)

In △ABC above,

 

a = 35 cm

b = 59 cm

C = 61º

 

Use a trigonometrical formula, to calculate its area in cm2 to 3 s.f.

 

(Just write the number)

In △ABC above,

 

c = 22 cm

b = 35 cm

A = 40º

 

Use a trigonometrical formula, to calculate its area in cm2 to 3 s.f.

 

(Just write the number)

In △ABC above,

 

c = 14 cm

a = 9.5 cm

B = 80.5º

 

Use a trigonometrical formula, to calculate its area in cm2 to 3 s.f.

 

(Just write the number)

In △ABC above,

 

a = 12 cm

b = 11.5 cm

C = 115º

 

Use a trigonometrical formula, to calculate its area in cm2 to 3 s.f.

 

(Just write the number)

In △ABC above,

 

a = 7.5 cm

b = 5.2 cm

C = 65º

 

Use a trigonometrical formula, to calculate its area in cm2 to 3 s.f.

 

(Just write the number)

In △ABC above,

 

a = 31 mm

b = 74 mm

C = 122º

 

Use a trigonometrical formula, to calculate its area in cm2 to 3 s.f.

 

(Just write the number)

  • Question 1

In △ABC above,

 

b = 4 cm

c = 5 cm

A = 40º

 

Use a trigonometrical formula, to calculate its area in cm2 to 3 s.f.

 

(Just write the number)

CORRECT ANSWER
6.43
EDDIE SAYS
Area = ½ × 4 × 5 × sin40°
  • Question 2

In △ABC above,

 

a = 4 cm

b = 6 cm

C = 55º

 

Use a trigonometrical formula, to calculate its area in cm2 to 3 s.f.

 

(Just write the number)

CORRECT ANSWER
9.83
EDDIE SAYS
Area = ½ × 4 × 6 × sin55°
  • Question 3

In △ABC above,

 

a = 4.5 cm

c = 6 cm

B = 85º

 

Use a trigonometrical formula, to calculate its area in cm2 to 3 s.f.

 

(Just write the number)

CORRECT ANSWER
13.4
EDDIE SAYS
Area = ½ × 4.5 × 6 × sin85°
  • Question 4

In △ABC above,

 

a = 6.2 cm

b = 7 cm

C = 125º

 

Use a trigonometrical formula, to calculate its area in cm2 to 3 s.f.

 

(Just write the number)

CORRECT ANSWER
17.8
EDDIE SAYS
Area = ½ × 6.2 × 7 × sin125°
  • Question 5

In △ABC above,

 

a = 35 cm

b = 59 cm

C = 61º

 

Use a trigonometrical formula, to calculate its area in cm2 to 3 s.f.

 

(Just write the number)

CORRECT ANSWER
903
EDDIE SAYS
Area = ½ × 35 × 59 × sin61°
  • Question 6

In △ABC above,

 

c = 22 cm

b = 35 cm

A = 40º

 

Use a trigonometrical formula, to calculate its area in cm2 to 3 s.f.

 

(Just write the number)

CORRECT ANSWER
247
EDDIE SAYS
Area = ½ × 35 × 22 × sin40°
  • Question 7

In △ABC above,

 

c = 14 cm

a = 9.5 cm

B = 80.5º

 

Use a trigonometrical formula, to calculate its area in cm2 to 3 s.f.

 

(Just write the number)

CORRECT ANSWER
65.6
EDDIE SAYS
Area = ½ × 9.5 × 14 × sin80.5°
  • Question 8

In △ABC above,

 

a = 12 cm

b = 11.5 cm

C = 115º

 

Use a trigonometrical formula, to calculate its area in cm2 to 3 s.f.

 

(Just write the number)

CORRECT ANSWER
62.5
EDDIE SAYS
Area = ½ × 12 × 11.5 × sin115°
  • Question 9

In △ABC above,

 

a = 7.5 cm

b = 5.2 cm

C = 65º

 

Use a trigonometrical formula, to calculate its area in cm2 to 3 s.f.

 

(Just write the number)

CORRECT ANSWER
17.7
EDDIE SAYS
Area = ½ × 7.5 × 5.2 × sin65°
  • Question 10

In △ABC above,

 

a = 31 mm

b = 74 mm

C = 122º

 

Use a trigonometrical formula, to calculate its area in cm2 to 3 s.f.

 

(Just write the number)

CORRECT ANSWER
9.73
EDDIE SAYS
Area = ½ × 3.1 × 7.4 × sin122°
---- OR ----

Sign up for a £1 trial so you can track and measure your child's progress on this activity.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Start your £1 trial

Start your trial for £1