Sine, Cosine Rule & Area of Triangles (AQA GCSE Maths)

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

is a triangle.

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

The diagram shows triangle .

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

is a triangle.
is a point on .
Angle = 45°
Angle = 80°
 = 7.4cm
 = 5.8 cm

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

is a triangle.

= 8.4m
Angle = 40°

The area of the triangle = 100 m².

Work out the length of .
Give your answer correct to 3 significant figures.
You must show all your working.

In triangle ,

 = 8.7 cm
 = 5.2 cm
Angle = 32°

Assuming that angle is an acute angle,
calculate the area of triangle .
Give your answer correct to 3 significant figures.

If you did not know that angle is an acute angle, what effect would this have on your calculation of the area of triangle ?

The diagram shows the triangle .

Angle  

The area of triangle

Show that   

is an isosceles triangle.

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

A shape is made by joining triangle to a semicircle with diameter .

Work out the total area of the shape.

Here is a triangular sail.

Vicky needs to buy waterproofing liquid for the sail.

She will put 3 coats of liquid on each side of the sail.
A litre of liquid covers 8.5 square metres of sail.

How many 1-litre bottles of liquid does Vicky need?

Another sail is joined to the first sail as shown.

is an acute angle.

Work out the size of angle .

Here is a triangle

The length and the angles and are each given correct to 2 significant figures.

Calculate the upper bound for the length .
Give your answer correct to one decimal place.
Show your working clearly.

....................................................... cm

Here is a quadrilateral .

Angle  is acute.

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

The diagram shows triangle ABC with D on AC and E on AB.
DE is a straight line.

AD = 28 m, AE = 41 m, DE = 22 m and BC = 64 m.

Calculate the length CD.

....................................................... m

The diagram shows some land in the shape of a quadrilateral, ABCD.

AB = 3km, AD = 5km, CD = 12km and angle BAC = 30°.

The land is sold for £10 million per square kilometre.

Calculate the total cost of the land.

£ .............................................. million

The area of triangle is m².

Calculate the value of .
Give your answer correct to significant figures.

and are triangles.

The area of triangle is 56 m²

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

is a parallelogram.

= 9 cm
 = 11 cm
Angle = 100°

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

is an acute-angled triangle.
= 7cm
 = 8cm

The area of triangle is 18 cm².

Work out the size of angle .
Give your answer correct to 3 significant figures.
You must show all your working.

The diagram shows a hexagon .

and are congruent parallelograms where 
is the point on and  is the point on such that 

Given that angle 

prove that  

is an acute angled triangle.

The area of triangle is 19 cm².

Work out the size of angle .
Give your answer correct to 3 significant figures.

is a triangle.
is a point on .

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

In this question, all lengths are in centimetres.

is a point on a circle, centre .
is a point on a different circle, centre .

The equation of the larger circle is    

radius of smaller circle : radius of larger circle   = 4 : 5

Work out the size of angle

............................................ degrees

The area of this triangle is 

Work out the value of .
Give your answer in the form  where  and  are integers greater than 1.

The diagram shows a logo.

and are congruent triangles.
is a sector of a circle, centre .

Show that the area of the logo is 510 cm² to 2 significant figures.

The diagram shows triangle

Given that angle is obtuse, work out the area of triangle .
Give your answer correct to 3 significant figures.

The diagram shows triangle

correct to one decimal place
     correct to the nearest whole number
   correct to the nearest whole number

Calculate the upper bound for the value of
Show your working clearly.
Give your answer correct to 3 significant figures.

is a quadrilateral where and are points on a circle.



Angle
Angle

Work out the perimeter of quadrilateral .
Give your answer correct to one decimal place.

....................................................... cm

Here is a triangle .

The perimeter of the triangle is .

Given that 
find the value of .
Show your working clearly.

The diagram shows a regular octagon 

Each side of the octagon has length 

Find the area of the shaded region 
Give your answer correct to the nearest 

.............................................