1. EVERYTHING YOU NEED TO KNOW TO GET A GRADE C
GEOMETRY & MEASURES
(FOUNDATION)
Part 1

2. Rhombus
Trapezium
Rectangle
Rhombus

3. Rhombus

4. Parallelogram
Rhombus
Trapezium or Right-angle Trapezium

5. 30 Base angles in a kite are equal
Opposite angles in a rhombus are equal
110°
250°
Base angles in a kite are equal
Angles around a point sum to 360°
Angles in a kite sum to 360° 30

6. Kite
Trapezium

7. Replace a with 3 and b with 5.2
P = 2 x x 5.2
P =
16.4
Total areas of both shapes are equal to one as shown.

8. Equilateral triangle Rhombus 2
(Fits on top of itself twice through a full turn)

9. Can choose either as your answer
5cm
5cm
Can choose either as your answer
3cm
3cm
9cm
5cm
Any two of rectangle, parallelogram, kite or arrowhead
The 3cm and 5cm rods would not meet
when joined with the 9cm rod.

10. In an isosceles triangle, the base angles are the same
Angles in a triangle sum to 180° 80 20 50 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

11. Angles in a triangle add to 180°
Isosceles Triangle
Angles in a triangle add to 180°
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

12. Angles in a triangle add to 180°
27°
27°
153°
180° - 126° = 54°
54° ÷ 2 = 27°
153° because angles on a straight line add up to 180° 27
153

13. 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
Base angles are the same in an isosceles triangle
65°
65°
70°
50°
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° 65
Both base angles are equal
180° - 50° = 130°
130° ÷ 2 = 65°

14. Angles on a straight line add to 180°
180° - 48° = 132°
132° ÷ 2 = 66°
Angles on a straight line add to 180°
180° - 66° = 114°
66°
66°
114°
114
A quadrilateral is made up of two triangles
180°
Angles is a triangle add up to 180°
180° + 180° = 360°
180°

15. Two exterior angles joined together
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

16. All the angles and sides are the same in a regular pentagon
Exterior angle
72°
36°
LEARN OFF BY HEART
Interior angle
108°
36°
= 72°
Angles on a straight line add up 180°
Interior angle = 180° - 72°
= 108°
Base angles in a isosceles triangle are the same
180° - 108°
= 72° 36

17. 20 Interior angle LEARN OFF BY HEART Exterior angle
Angles on a straight line add up 180°
Exterior angle = 180° - 162°
= 18°
= 20 20

18. Sum of interior angles = (number of sides – 2) x 180°
Decagon
Pentagon
LEARN OFF BY HEART
Interior angle
Interior angle
108°
144°
Sum of interior angles = (number of sides – 2) x 180°
108°
36°
144°
36°
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

19. Sum of interior angles = (number of sides – 2) x 180°
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

20. As worked out in part (a)
LEARN OFF BY HEART
Sum of interior angles of an octagon = (8 – 2) x 180°
= 6 x 180°
= 1080°
= 135°
Sum of interior angles = (number of sides – 2) x 180°
135
135°
135°
135°
As worked out in part (a)
= 135°
Angles around a point add up to 360°
360° - 135° - 135°
= 90°
Therefore, as all angles are 90° PQRS is a square

21. 2.5 -1

22. Alternate angles are equal
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.

23. Alternate angles are equal
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.

24. 41°
113° 41
Interior angles add up to 180°
180° - 67°
= 113°
113

25. OTHER ANSWERS ALSO ALLOWED Perimeter is the length around a shape2
4cm
3cm
3cm
OTHER ANSWERS ALSO ALLOWED
4cm
6cm
2cm
2cm
6cm
Perimeter of rectangle A =
14cm
Perimeter is the length around a shape
Perimeter of rectangle B =
16cm
Difference =
16cm - 14cm 2

26. Perimeter is the length around a shape
6cm
4cm
4cm
Perimeter is the length around a shape
6cm
Perimeter of rectangle =
6cm + 4cm + 6cm + 4cm 20
Square has 4 equal sides
3cm for each side

27. OTHER ANSWERS ALSO ALLOWEDx x x x
Because two lengths of 12cm makes 24cm which is more than the perimeter
As evident from the rectangle drawn for part (a)

28. Find the only rectangle which has a perimeter of 26cm
40cm
1cm
20cm
2cm
10cm
4cm
8cm
5cm
Find the only rectangle which has a perimeter of 26cm 8 5

29. Split compound shape into two rectangles
Kilo means a thousand
1km = 1000m
1000m
Area =
Length x Width
= 1000m x 10m
Split compound shape into two rectangles
Rectangle A
200m
Rectangle B
Area of rectangle A =
100 x 30
Area of rectangle B =
200 x a
200a = 10000 35
200a = 7000

30. Count the number of squares to find the areaC B E

31. Shaded Area = Area of square – Area of circle
30cm
Diameter
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 =
3574

32. equal to less than (because the length around the shape is the same)
(because more than half the rectangle is unshaded)

33. 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 =
Shaded area =
Area of four triangles = 82

34. 900 50 60 Area of small square = 30cm x 30cm Length of large square = 50
Area of floor =
300cm x 180cm
Number of small tiles needed =
Number of small tiles needed = 60

35. 8 A and C C and D Perimeter is the length around a shape
Perimeter B = 9cm
Perimeter A = 10cm
Perimeter is the length around a shape
2cm
2cm
2cm
2cm
Perimeter C = 10cm
Perimeter of D =
2cm + 2cm + 2cm + 2cm 8
A and C
Area is the space inside a shape
C and D

36. Shaded Area = Area of big square – Area of two smaller squares
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 =
Shaded Area =
Fraction shaded =
Unshaded

37. 6

38. A, B and E