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EVERYTHING YOU NEED TO KNOW
TO GET A GRADE C
GEOMETRY & MEASURES
(FOUNDATION)
Part 1
Rhombus
Trapezium
Rectangle
Rhombus
Rhombus
Parallelogram
Rhombus
Trapezium or Rightangle Trapezium
110°
250°
Base angles in a kite are equal
Opposite angles in a rhombus are equal
Angles around a point sum to 360°
Angles in a kite sum to 360°
30
Kite
Trapezium
Replace a with 3 and b with 5.2
P = 2 x 3 + 2 x 5.2
P = 6 + 10.4
Total areas of both shapes are equal to
one as shown.
16.4
Equilateral triangle
Rhombus
2
(Fits on top of itself twice through a full turn)
5cm
5cm
3cm
3cm
9cm
Can choose either as
your answer
5cm
Any two of rectangle, parallelogram, kite or arrowhead
The 3cm and 5cm rods would not meet
when joined with the 9cm rod.
In an isosceles triangle, the base angles are the same
Angles in a
triangle sum to
180°
80
50
20
50
Each angle is 60° in an
equilateral triangle
120° because angles on a straight line add to 180°
30° because angles in a right angle add to 90°
Base angles are both 30° so ABD is an isosceles triangle
Isosceles Triangle
35°
73°
107°
73°
107° because angles on a straight line add up to 180°
180° - 34° = 146°
146° ÷ 2 = 73°
73
y = 180° - 107° - 38° = 35°
35
No, because 38° is not equal to 35°. Therefore, it is not
an isosceles triangle
Angles in a triangle
add to 180°
Angles in a triangle
add to 180°
153°
27°
27°
180° - 126° = 54°
54° ÷ 2 = 27°
153° because angles on a straight line
add up to 180°
27
153
Base angles are the same in
an isosceles triangle
80°
Means work out angle A in triangle ABC
Angles in a triangle add to 180°
180° - 80° - 80° = 20°
20
65°
50°
Base angles are the same in
an isosceles triangle
65°
70°
40°
Means work out angle R in triangle PQR
Angles in a triangle add to 180°
180° - 70° - 70° = 40°
A right angle is 90°
90° - 40° = 50°
Both base angles are equal
180° - 50° = 130° 130° ÷ 2 = 65°
65
66°
66°
180° - 48° = 132° 132° ÷ 2 = 66°
Angles on a straight line add to 180°
180° - 66° = 114°
114°
114
A quadrilateral is made up of two triangles
180°
180°
Angles is a triangle add up to 180°
180° + 180° = 360°
LEARN OFF BY HEART
(because the exterior angles add up to 360°)
Exterior angle = 72°
Two exterior
angles joined
together
72°
As worked out in part (a)
72°
144
All the angles and
sides are the same in
a regular pentagon
Exterior
72°
angle
Exterior
72°
angle
36°
LEARN OFF BY HEART
Interior
108°
angle
Exterior
72°
angle
36°
Exterior
72°
angle
Exterior
72°
angle
= 72°
Angles on a straight line add up 180°
Interior angle = 180° - 72° = 108°
Base angles in a isosceles triangle are the same
36
180° - 108° = 72°
Interior angle
LEARN OFF BY HEART
Exterior angle
Angles on a straight line add up 180°
Exterior angle = 180° - 162° = 18°
= 20
20
Decagon
LEARN OFF BY HEART
Pentagon
Interior
108°
angle
Interior
144°
angle
Sum of interior angles = (number of sides – 2) x 180°
144°
Sum of interior angles of an decagon = (10 – 2) x 180° = 8 x 180° = 1440°
= 144°
Sum of interior angles of a pentagon = (5 – 2) x 180°= 3 x 180° = 540°
= 108°
Angles around a point add up to 360°
360° - 144° - 108° = 108°
Base angles in a isosceles triangle are the same
180° - 108° = 72°
72° ÷ 2 = 36°
144° + 36° = 180° (Angles on a straight line add up to 180°)
Therefore, ABC lie on a straight line
LEARN OFF BY HEART
Sum of interior angles = (number of sides – 2) x 180°
Hexagon
Interior
angle
120°
Square
60°
Square
60°
60°
Sum of interior angles of an hexagon = (6 – 2) x 180° = 4 x 180° = 720°
= 120°
Angles around a point add up to 360°
360° - 120° - 90° - 90°= 60°
Base angles are the same
180° - 60° = 120°
120° ÷ 2= 60°
Therefore, as all angles are 60° AHJ is equilateral
Sum of interior angles of an octagon = (8 – 2) x 180° = 6 x 180° = 1080°
= 135°
LEARN OFF BY HEART
Sum of interior angles = (number of sides – 2) x 180°
135
135° 135°
135°
135°
135°
135°
135° 135°
= 135°
Angles around a point add up to 360°
360° - 135° - 135° = 90°
Therefore, as all angles are 90° PQRS is a square
As worked out in part (a)
2.5
-1
70°
40°
70°
Alternate angles are equal
Angles on a straight line add up 180°
180° - 110° = 70°
Angles in a triangle add up 180°
180° - 40° - 70° = 70°
As both base angles are 70°, triangle BEF is isosceles.
55°
55°
Alternate angles are equal
Angles in a triangle add up 180°
180° - 70° - 55° = 55°
As both base angles are 55°,
triangle ABC is isosceles.
41°
113°
41
Interior angles add up to 180°
180° - 67° = 113°
113
2
4cm
3cm
3cm
4cm
6cm
2cm
2cm
OTHER
ANSWERS
ALSO
ALLOWED
6cm
Perimeter of rectangle A 14cm
=Perimeter of rectangle B = 16cm
Difference = 16cm - 14cm
2
Perimeter is the
length around a
shape
6cm
4cm
Perimeter is the
length around a
shape
4cm
6cm
Perimeter of rectangle = 6cm + 4cm + 6cm + 4cm
20
Square has 4
equal sides
3cm for each side
x
x
x
x
OTHER
ANSWERS
ALSO
ALLOWED
Because two lengths of 12cm makes
24cm which is more than the perimeter
As evident from the rectangle drawn for part (a)
20cm
40cm
1cm
1cm
2cm
20cm
40cm
10cm
4cm
8cm
4cm
10cm
2cm
5cm
5cm
8cm
Find the only rectangle
which has a perimeter
of 26cm
8
5
Kilo means a thousand
1km = 1000m
1000m
Area = Length x Width
= 1000m x 10m
Rectangle A
Split compound shape
into two rectangles
200m
Rectangle B
Area of rectangle A = 100 x 30
Area of rectangle B = 200 x a
35
200a + 3000 = 10000
200a
= 7000
Count the number of
squares to find the area
C
B
E
Shaded Area = Area of square – Area of circle
LEARN THE FORMULAE
OFF BY HEART
Area of square = length x width
= 80cm x 80cm
Area of circle =
= 3.14 x 30cm x 30cm
Area shaded = 6400 - 2826
3574
equal to
less than
(because the length around the shape is the same)
(because more than half the rectangle is unshaded)
10cm
10cm
Shaded Area = Area of big square ABCD – Area of the 4 congruent (identical) triangles
Area of big square = length x width
= 10cm x 10cm
Area of one triangle =
Area of one triangle =
Area of one triangle =
Area of four triangles =
82
Shaded area =
Area of small square = 30cm x 30cm
900
Length of large square =
50
Area of floor = 300cm x 180cm
Number of small tiles needed =
Number of small tiles needed =
60
Perimeter B = 9cm
Perimeter A = 10cm
Perimeter is the
length around a
shape
Perimeter C = 10cm
Perimeter of D = 2cm + 2cm + 2cm + 2cm
8
A and C
C and D
Area is the space
inside a shape
Shaded Area = Area of big square – Area of two smaller squares
Area of big square = length x width = 12cm x 12cm
Area of one small square = length x width = 4cm x 4cm
Area of both squares =
Shaded Area =
Area of big square = length x width
Area of one small square = length x width
Area of both squares =
Unshaded
Shaded Area =
Fraction shaded =
6
A, B and E