Lesson Notes By Weeks and Term v5 - Grade 7
Geometry of 2D shapes and 3D objects (Grade 7) – Week 5 focus
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Geometry of 2D shapes and 3D objects (Grade 7) – Week 5 focus
Download the Lessonotes Mobile South Africa app for faster lesson access on Android and iPhone.
Subject: Mathematics
Class: Grade 7
Term: 3rd Term
Week: 5
Theme: General lesson support
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This week, we delve into the exciting world of geometry, focusing on understanding the properties of 2D shapes (like squares, triangles, and circles) and 3D objects (like cubes, pyramids, and cylinders). Geometry is crucial because it helps us understand the world around us. From the design of buildings and roads to the patterns in nature and the packaging of our favourite snacks, geometry plays a vital role. In the South African context, understanding geometry can help with tasks like planning a garden, calculating the amount of materials needed for a home improvement project, or even understanding the shapes and patterns found in traditional art and crafts.
2.1. 2D Shapes: A Review Definition: 2D shapes are flat shapes that have only two dimensions: length and width. They are also called plane figures.
Examples: Square: A quadrilateral with four equal sides and four right angles (90°).
Rectangle: A quadrilateral with two pairs of equal sides and four right angles (90°).
Triangle: A polygon with three sides and three angles.
Different types of triangles exist: Equilateral Triangle:* All three sides are equal, and all three angles are equal (60° each).
Isosceles Triangle:* Two sides are equal, and the angles opposite those sides are also equal.
Scalene Triangle:* All three sides are different lengths, and all three angles are different sizes.
Right-angled Triangle:* One angle is a right angle (90°).
Circle: A set of points equidistant from a central point.
Parallelogram: A quadrilateral with two pairs of parallel sides. Opposite sides are equal, and opposite angles are equal.
Trapezium (or Trapezoid): A quadrilateral with only one pair of parallel sides.
Kite: A quadrilateral with two pairs of adjacent sides that are equal in length.
Rhombus: A quadrilateral with four equal sides, but its angles are not necessarily right angles. A rhombus is a special type of parallelogram.
Perimeter: The total distance around the outside of a 2D shape.
Example: Square with side length 5cm. Perimeter = 4 side = 4 5cm = 20cm
Example: Rectangle with length 8cm and width 3cm. Perimeter = 2 (length + width) = 2 (8cm + 3cm) = 22cm Area: The amount of surface a 2D shape covers.
Example: Square with side length 5cm. Area = side side = 5cm 5cm = 25cm²
Example: Rectangle with length 8cm and width 3cm. Area = length width = 8cm 3cm = 24cm²
Example: Triangle with base 6cm and height 4cm. Area = 1/2 base height = 1/2 6cm 4cm = 12cm² 2.2. 3D Objects: Exploring Space Definition: 3D objects are solid shapes that have three dimensions: length, width, and height (or depth).
Examples: Cube: A 3D object with six square faces. All sides are equal in length.
Cuboid: A 3D object with six rectangular faces. It is also called a rectangular prism.
Sphere: A 3D object where every point on the surface is equidistant from the center. Like a ball.
Cylinder: A 3D object with two circular bases and a curved surface connecting them.
Cone: A 3D object with a circular base and a single vertex (point) at the top.
Pyramid: A 3D object with a polygonal base and triangular faces that meet at a common vertex (apex). Pyramids are named according to the shape of their base (e.g., square pyramid, triangular pyramid).
Surface Area: The total area of all the faces of a 3D object.
Example: Cube with side length 4cm. Each face has an area of 4cm 4cm = 16cm². Since there are 6 faces, the surface area is 6 16cm² = 96cm²
Example: Cuboid with length 5cm, width 3cm, and height 2cm. The surface area is 2(lengthwidth + lengthheight + widthheight) = 2(5cm3cm + 5cm2cm + 3cm2cm) = 2(15cm² + 10cm² + 6cm²) = 2(31cm²) = 62cm² Volume: The amount of space a 3D object occupies.
Example: Cube with side length 4cm. Volume = side side side = 4cm 4cm 4cm = 64cm³
Example: Cuboid with length 5cm, width 3cm, and height 2cm. Volume = length width height = 5cm 3cm 2cm = 30cm³ 2.
3. Nets of 3D Objects A net is a 2D shape that can be folded to form a 3D object. Visualizing nets helps understand the surface area of 3D objects.
Example: A cube net consists of six squares connected in such a way that they can be folded to form a cube.*
Example: A cuboid net consists of six rectangles connected in such a way that they can be folded to form a cuboid.* Guided Practice (With Solutions)
Question 1: A rectangular garden in Soweto is 12 meters long and 8 meters wide. (a) What is the perimeter of the garden? (b) What is the area of the garden?
Solution: (a)
Perimeter: Perimeter = 2 (length + width) = 2 (12m + 8m) = 2 * 20m = 40 meters.
Commentary: This calculation applies the standard formula for the perimeter of a rectangle. Remember to include the units (meters) in your answer. (b)
Area: Area = length width = 12m 8m = 96 square meters (m²).
Commentary: This calculation applies the standard formula for the area of a rectangle. Remember to include the correct units (square meters) in your answer.
Question 2: A square-shaped paving stone has a side length of 30 cm. (a) What is the perimeter of the paving stone? (b) What is the area of the paving stone?
Solution: (a)
Perimeter: Perimeter = 4 side = 4 30cm = 120 cm.
Commentary: The perimeter of a square is four times the length of one of its sides. (b)
Area: Area = side side = 30cm 30cm = 900 cm².
Commentary: The area of a square is the side length squared.
Question 3: A farmer in KwaZulu-Natal wants to build a storage container in the shape of a cube. If each side of the cube is 2.5 meters long, what is the volume of the container?
Solution: Volume = side side side = 2.5m 2.5m 2.5m = 15.625 m³.
Commentary: The volume of a cube is found by cubing the length of its side. The units are cubic meters.