Objective: to be able to calculate the area of a triangle using trigonometry (Grade A)

By the end of the lesson:All: will be to identify when to find the area of a triangle using

Most: will be able to calculate the area of a triangle using the formula

Some: will be to calculate GCSE area of a triangle problems using

Trigonometry

(Up to Grade A*)

StarterCalculate the area of the following

shapesGreen Red

Starter - Answers

Green Red

Area = 24cm2

Area = 2.4mm2

Area = 35cm2

Area = 50cm2

Calculate the Area of this triangle

What do we need to know to calculate the area of this triangle?

Can we calculate this?

What can we use to find h?

×8 ×8

This is found by trig

How the ABC’s work

A

C

B

a

c

b

A

C

B

a

c

b

The Formula

Formula

Page

You do need to learn this

as its no longer given.

Task 1For which of the following questions is it possible to find the area of the triangle using (Hint: look for an angle between 2 given

sides)

Extension: create your own example of a question that could solved using the formula we have learnt

Task 1 - Solutions

Examples

Task 2 – Give your answers to 3 significant figures

Extension:

Task 2 - Solutions

a = 9.58 cm2

b = 44.5 cm2

c = 26.2 cm2

d = 17.3 cm2

e = 63.3 cm2

f = 28.7 cm2

Extension

a = 202cm2

b = 72.2cm2

In your own words

Explain how you calculate the area of a triangle using trigonometry?

Use the wordsAreaAngleSidesSine

Finding missing side or angle given the area.

Task 3 – Give your answers to 3 significant figures

Task 3 - Solutions

a = 3.90 cm

b = 7.39 cm

x = 56.4o

y = 57.1o

Task 4 – Past GCSE Questions

Complete the following past GCSE questions

There are green, amber and red sections

(Red Grade A*)(Green and Amber Grade A)

Task 2 – Solutions

Green Amber Red

area = 19.31851653cm2

area = 19.3cm2 (3 s.f.)

area = 2068.319996m2

area = 2070m2 (3 s.f)

x = 9.118028228cm

x = 9.12cm (3 s.f.)

area = 10.87606829m2

area = 10.9m2 (3 s.f)

area = 1.771010916cm2

area = 1.78cm2 (3s.f.)

area = 119.3241659m2

area = 119m2 (3 s.f)

Green 1

Green 2

Amber 1

Amber 2

Red 1

Red 2

To finish the lesson

In your own words, explain when you would apply

to calculate the area, missing angle or missing side

of a triangle.

Further GCSE Questions