Year 5 Exam > Year 5 Notes > Year 5 Mathematics IGCSE (Cambridge) > Chapter Notes: Angles and Shapes, Perimeter and Area
Angles and Shapes, Perimeter and Area Chapter Notes | Year 5 Mathematics IGCSE (Cambridge) PDF Download
Perimeter and Area
- Perimeter is the total distance around the boundary of a shape, calculated by summing the lengths of all sides.
- Area is the measure of the surface enclosed by a shape, typically calculated in square units.
- For regular polygons, all sides are equal, simplifying perimeter calculation:
- Example: A square with side length 5 cm has perimeter 4 × 5 = 20 cm.
- Compound shapes are formed by combining simpler shapes, requiring careful measurement of all external sides for perimeter and division into simpler shapes for area.
- Example: Compound shape A with sides 8, 1, 4, 5, 3:
- Perimeter: 8 + 1 + 4 + 5 + 3 = 21 units.
- Example: Compound shape B with sides 8, 7, 1, 3, 3:
- Perimeter: 8 + 7 + 1 + 3 + 3 = 22 units.
- Area calculation methods for compound shapes:
- Divide the shape into rectangles or triangles and sum their areas.
- Use grid paper to count squares or measure dimensions accurately.
- Shapes with equal perimeters can have different areas, and vice versa, depending on their dimensions.
- Example: A rectangle with dimensions 4 cm by 12 cm:
- Perimeter: 2 × (4 + 12) = 32 cm.
- Area: 4 × 12 = 48 cm².
- Example: An equilateral triangle with perimeter 45 cm:
- Side length: 45 ÷ 3 = 15 cm.
3D Shapes
- A net is a 2D shape that can be folded to form a 3D shape.
- Open and closed shapes:
- An open cube net lacks one face, forming a cube with one missing side.
- A closed cube net has six squares arranged to form a complete cube.
- Example: A cube net consists of 6 squares, typically arranged in a cross pattern for a closed cube.
- A cuboid net consists of 6 rectangles, arranged to form a box with different dimensions for length, width, and height.
- Sketching 3D shapes:
- Use dotty paper to draw cubes and cuboids, ensuring parallel lines and consistent angles to represent depth.
- Shapes can be sketched from different angles to show perspective (e.g., front, top, side views).
- 3D shapes with curved surfaces (e.g., cylinders, cones, spheres) can be sketched, focusing on their circular or curved features.
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FAQs on Angles and Shapes, Perimeter and Area Chapter Notes - Year 5 Mathematics IGCSE (Cambridge)
| 1. What is the formula to calculate the perimeter of a rectangle? |  |
Ans. The formula to calculate the perimeter of a rectangle is P = 2(l + w), where P is the perimeter, l is the length, and w is the width of the rectangle.
| 2. How do you find the area of a triangle? | |
Ans. The area of a triangle can be calculated using the formula A = 1/2(b * h), where A is the area, b is the base length, and h is the height of the triangle.
| 3. What is the difference between perimeter and area? | |
Ans. Perimeter is the total distance around a two-dimensional shape, measured in linear units, while area is the measure of the space inside a shape, measured in square units.
| 4. How can I calculate the area of a circle? | |
Ans. The area of a circle can be calculated using the formula A = πr², where A is the area, π (pi) is approximately 3.14, and r is the radius of the circle.
| 5. What are the units used for measuring area and perimeter? | |
Ans. Perimeter is measured in linear units such as meters, centimeters, or feet, while area is measured in square units such as square meters, square centimeters, or square feet.
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