Calculate the area of triangles, rectangles and parallelograms

1

Find the areas of the triangles.

a) c)

cm

2

cm

2

b) d)

cm

2

m

2

Eva is working out the area of the triangle.

What mistake has Eva made?

3

Find the areas of the parallelograms.

a) b)

cm

2

mm

2

4

The two rectangles have the same area.

Work out the width of rectangle B.

cm

Calculate the area of triangles,

rectangles and parallelograms

The base is 7.8 cm

and the length of one side

is 6.3 cm. I multiply and

then divide by 2

6 cm

5 cm

10 mm

4 mm

5 mm

12 cm

5 cm

8 cm

4 cm

7.8 cm

6.3 cm

B

8 cm

6 m

8 m

10 m

6 cm

9 cm

A

3 cm

12 cm

8

A rectangle is split into three triangles.

One of the triangles is shaded.

What is the ratio of shaded to non-shaded parts of the shape?

:

9

A logo is made from four identical right-angled triangles.

Find the area of one of the triangles.

5

The area of the triangle is 26 cm

2

What is its height?

h = cm

6

Work out the areas of the shapes.

a) b) c)

7

These three shapes all have the same area.

Find the missing values.

13 cm

h

1

2

m

8 cm

12 cm

7 cm

16 cm

21 cm

700 m

1.1 km

12 cm

9 cm

8 cm

4 mm

1

4

cm

1

Amir and Rosie are working out the area of this trapezium.

a) Use Amir’s method to ﬁnd the area of the trapezium.

cm

2

b) Use Rosie’s method to ﬁnd the area of the trapezium.

cm

2

Whose method do you prefer?

2

Find the area of each trapezium.

a)

cm

2

b)

m

2

c)

cm

2

d)

mm

2

Calculate the area of a trapezium

I will divide the

shape into a rectangle

and triangle, and work out

the area of each one.

I will just use the formula

for the area of a trapezium.

Amir

Rosie

8 cm

5 cm

4 cm

6 cm

4 cm

5 cm

4 m

1 m

4 m

8 cm

7 cm

6 cm

3.5 mm

12.4 mm

6 mm

5

The area of each trapezium is 20 cm

2

Find and label the missing lengths.

a) b)

6

The area of the trapezium is 24 cm

2

Write three possible pairs of values of x and y.

x = cm y = cm

7

Prove the statement.

The formula for a trapezium is equal to the area of

a parallelogram when the lengths of a and b are equal.

3

Work out the area of each trapezium.

a)

b)

c) Discuss with a partner what mistakes could be made when working out

the areas in parts a) and b).

4

Explain why these trapeziums all have the same area.

8 cm 9 cm 6.8 cm

4 cm 3 cm 5.2 cm

6 cm

5 cm

11.5 cm

8.5 cm

y

x

6 cm

b

a

h

7 cm

10 cm

5 cm

4 cm

7 m

2 m

120 cm

1

Work out the unknown lengths and then ﬁnd the perimeter of

each shape.

a)

perimeter =

cm

b)

perimeter =

cm

2

Work out the area of each shape.

a)

area =

m

2

b)

area =

cm

2

3

Is Mo correct?

Explain your answer.

4

Some stickers have the letter H on them.

What is the area of the letter H?

mm

2

Calculate the perimeter and area

of compound shapes (1)

You can’t work out

the perimeter of this shape

as you don’t know the

lengths of all the sides.

7 cm

3 cm

4 cm

5 cm

7 m

3 m

4 m

9 m

7 cm 7 cm

25 cm

4 cm

10 cm

2.2 cm

6.1 cm

7.3 cm

1.7 cm

5 mm 5 mm

18 mm

14 mm

6 mm

3 cm

10 cm

2 cm

6 cm

4 cm

5

Find the area of each compound shape.

a)

cm

2

b)

cm

2

c)

m

2

d)

cm

2

6

Dani makes a picture of a tree.

The tree is made up of a green triangle,

two congruent green trapeziums

and a brown square.

Find the area of the green part of the tree.

cm

2

7

What fraction of the shape is shaded?

8

Which hexagon has the greatest area?

6 m

11 m

8 m

5 m

8 cm

5 cm

1.4 cm

1.8 cm

2.3 cm 1.9 cm

7 cm

4 cm

6 cm

12 cm

11 cm

7 cm

4 cm

10 mm

12 mm

18 mm

4 cm

5 cm

3 cm

4 cm

5 cm

3 cm

2 cm

Understand π as a ratio

1

a) What is the length of the square?

b) What is the perimeter of the square?

c) What is the ratio of length : perimeter of the square?

:

d) Will this ratio always be the same? Talk about it with a partner.

e) Will the ratio be the same for any other shapes? Why?

2

What is the diameter of each of these circles?

a) c)

diameter =

b) d)

diameter = diameter =

3

What is the diameter of the circle?

diameter =

How do you know? Talk about it with a partner.

6 cm

10 cm

12 cm

7 cm

6 cm

7.5 cm

2 mm

10 cm

2 mm

4

Write the ratio of diameter : circumference for each circle in the form 1 : n

a)

10 cm : 31.4 cm = 1 :

b)

20 cm : 62.8 cm =

:

c)

: = :

d)

: = :

e) What do you notice about your answers?

f) Complete the sentence.

For any circle, the ratio of diameter : circumference can be written as

1 :

, or more accurately 1 :

3

1

.

4

c

m

10 cm

6

2

.

8

c

m

6

.

2

8

m

2 mm

1

2

.

5

6

m

2 mm

10 cm

5

Complete this representation.

The circumference of a circle is equal to

C =

6

Calculate the circumference of the circles.

a) c)

C =

b) d)

C =

12 cm

� mm

8 cm

4 cm

diameter : circumference

1 : π

×

d :