(a) The diagram shows a shape on 1 cm² grid.
Work out the area of the shape.
(b) The diagram shows a rectangle.
Work out the perimeter of the rectangle.
(c) A square has an area of 841 cm².
Work out the length of one side of the square.
(d) The diagram shows a cuboid made from 1 cm³ cubes.
(i) Work out the volume of the cuboid.
(ii) Write down the dimensions of a different cuboid that can be made using all of the cubes.
(e) The diagram shows three small circles and one large circle. The large circle has radius 20 cm. The small circles each have radius 4 cm.
Work out the shaded area.
Give your answer in terms of π.
(f) The exterior angle of a 9-sided regular polygon is 40°.
(i) Work out the size of the interior angle of this polygon.
(ii) The diagram shows a regular pentagon inside part of a regular 9-sided polygon.
Work out the value of x.
▶️ Answer/Explanation
(a) Ans: 9.5 cm²
The shape consists of:
- A rectangle (6 cm × 1 cm = 6 cm²)
- Two full triangles (2 × 1 cm² = 2 cm²)
- One half triangle (0.5 cm²)
- One extra square (1 cm²)
Total area = 6 + 2 + 0.5 + 1 = 9.5 cm².
(b) Ans: 38 cm
Perimeter = 2 × (length + width) = 2 × (12 cm + 7 cm) = 38 cm.
(c) Ans: 29 cm
Side length = √Area = √841 = 29 cm.
(d)(i) Ans: 48 cm³
Volume = length × width × height = 8 × 2 × 3 = 48 cm³.
(d)(ii) Ans: 4 cm × 4 cm × 3 cm
Alternative dimensions using 48 cubes: 4 × 4 × 3 = 48 cm³.
(e) Ans: 352π cm²
Shaded area = Area of large circle (400π) – Area of 3 small circles (48π) = 352π cm².
(f)(i) Ans: 140°
Interior angle = 180° – exterior angle = 180° – 40° = 140°.
(f)(ii) Ans: 16°
Using the interior angles of pentagon (108°) and nonagon (140°): 2x + 108° = 140° ⇒ x = 16°.
(a) 
Find the perimeter of the triangle.
(b) The diagram shows a shape made from rectangles.
Calculate the area of the shape.
(c) The diagram shows a right-angled triangle ABC.
Calculate the area of the triangle.
(d) Calculate the volume of a sphere with diameter 5.25 cm.
[The volume, V, of a sphere with radius r is $V = \frac{4}{3}\pi r^3$.]
▶️ Answer/Explanation
(a) 21 cm
Simply add all sides: 10 + 7 + 4 = 21 cm.
(b) 118.1 cm²
Break into rectangles: (18.6×4) + (9.5×4.6) = 74.4 + 43.7 = 118.1 cm².
(c) 153.6 cm²
First find missing side: √(27.2²-24²) = 12.8 cm. Then area = ½×24×12.8 = 153.6 cm².
(d) 75.8 cm³
Radius = 5.25/2 = 2.625 cm. Volume = (4/3)π(2.625)³ ≈ 75.8 cm³.