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1 Findtheareasofthetriangles.
a) c)
cm2 cm2
b) d)
cm2 m2
2 Evaisworkingouttheareaofthetriangle.
WhatmistakehasEvamade?
3 Findtheareasoftheparallelograms.
a) b)
cm2 mm2
4 Thetworectangleshavethesamearea.
WorkoutthewidthofrectangleB.
cm
Calculate the areaof triangles, rectanglesandparallelograms
©WhiteRoseMaths2020
The base is 7.8 cm and the length of one side is 6.3 cm. I multiply and
then divide by 2
6cm
5cm
10mm
4mm5mm
12cm
5cm
8cm
4cm
7.8cm
6.3cm
B
8cm
6m
8m
10m
6cm
9cm
A3cm
12cm
8 Arectangleissplitintothreetriangles.
Oneofthetrianglesisshaded.
Whatistheratioofshadedtonon-shadedpartsoftheshape?
:
9 Alogoismadefromfouridenticalright-angledtriangles.
Findtheareaofoneofthetriangles.
©WhiteRoseMaths2020
5 Theareaofthetriangleis26cm2
Whatisitsheight?
h= cm
6 Workouttheareasoftheshapes.
a) b) c)
7 Thesethreeshapesallhavethesamearea.
Findthemissingvalues.
13cm
h
112
m
8cm
12cm
7cm
16cm
21cm
700m
1.1km
12cm
9cm
8cm
8cm
4mm
14
cm
1 AmirandRosieareworkingouttheareaofthistrapezium.
a) UseAmir’smethodtofindtheareaofthetrapezium.
cm2
b) UseRosie’smethodtofindtheareaofthetrapezium.
cm2
Whosemethoddoyouprefer?
2 Findtheareaofeachtrapezium.
a)
cm2
b)
m2
c)
cm2
d)
mm2
Calculate the areaofa trapezium
©WhiteRoseMaths2020
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
8cm
5cm
4cm
6cm
4cm
5cm
4m
1m
4m
8cm
7cm
6cm
3.5mm
12.4mm
6mm
5 Theareaofeachtrapeziumis20cm2
Findandlabelthemissinglengths.
a) b)
6 Theareaofthetrapeziumis24cm2
Writethreepossiblepairsofvaluesofxandy.
x= cm y= cm
x= cm y= cm
x= cm y= cm
7 Provethestatement.
Theformulaforatrapeziumisequaltotheareaof
aparallelogramwhenthelengthsofaandbareequal.
©WhiteRoseMaths2020
3 Workouttheareaofeachtrapezium.
a)
b)
c) Discusswithapartnerwhatmistakescouldbemadewhenworkingout
theareasinpartsa)andb).
4 Explainwhythesetrapeziumsallhavethesamearea.
8cm 9cm 6.8cm
4cm 3cm 5.2cm
6cm
5cm
5cm 11.5cm
8.5cm
y
x
6cm
b
a
h
7cm
10cm
5cm4cm
7m
2m
120cm
1 Workouttheunknownlengthsandthenfindtheperimeterof
eachshape.
a)
perimeter= cm
b)
perimeter= cm
2 Workouttheareaofeachshape.
a)
area= m2
b)
area= cm2
3
IsMocorrect?
Explainyouranswer.
4 SomestickershavetheletterHonthem.
WhatistheareaoftheletterH?
mm2
Calculate the perimeter andarea of compound shapes (1)
©WhiteRoseMaths2020
You can’t work out the perimeter of this shape
as you don’t know the lengths of all the sides.
7cm
3cm
4cm
5cm
7m
3m
4m
9m
7cm 7cm
25cm
4cm
10cm
2.2cm
6.1cm
7.3cm
1.7cm
5mm 5mm
18mm
14mm
6mm
3cm
10cm
2cm
6cm
4cm
5 Findtheareaofeachcompoundshape.
a)
cm2
b)
cm2
c)
m2
d)
cm2
6 Danimakesapictureofatree.
Thetreeismadeupofagreentriangle,
twocongruentgreentrapeziums
andabrownsquare.
Findtheareaofthegreenpartofthetree.
cm2
7 Whatfractionoftheshapeisshaded?
8 Whichhexagonhasthegreatestarea?
©WhiteRoseMaths2020
6m
11m
8m
5m
8cm
8cm
5cm
1.4cm
1.8cm
2.3cm 1.9cm
7cm
4cm
6cm
12cm
11cm7cm
4cm
10mm
12mm
18mm
4cm
5cm 3cm
3cm
4cm 5cm
3cm2cm
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 = diameter =
b) d)
diameter = diameter =
3
What is the diameter of the circle?
diameter =
How do you know? Talk about it with a partner.
© White Rose Maths 2019
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 :
© White Rose Maths 2019
31.4 cm
10 cm
62
.8 cm
6.28
mm
2 mm
12.5
6 mm
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 = C =
b) d)
C = C =
12 cm
12 cm � mm
8 cm
4 cm
diameter : circumference
1 : π
×
×
d :