Lesson Notes By Weeks and Term v5 - Grade 7
Geometry of 2D shapes and 3D objects (Grade 7) – Week 3 focus
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Geometry of 2D shapes and 3D objects (Grade 7) – Week 3 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: 3
Theme: General lesson support
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This week, we delve deeper into the fascinating world of geometry, focusing on 2D shapes and 3D objects. Understanding geometry is crucial not just for mathematics class, but also for navigating and understanding the world around us. From designing a shack with optimal space utilization (2D shapes for floor plans, 3D for the structure) to calculating the amount of paint needed for a classroom wall or understanding the packaging of the products we buy in shops, geometry is everywhere. In South Africa, with a strong focus on infrastructure development and resource management, understanding geometric principles is invaluable.
2.1 Quadrilaterals: A Deep Dive A quadrilateral is a closed, two-dimensional shape with four straight sides. Different types of quadrilaterals have unique properties: Parallelogram: A quadrilateral with two pairs of parallel sides. Opposite sides are equal in length, and opposite angles are equal.
Rectangle: A parallelogram with four right angles (90°). Opposite sides are equal in length. Diagonals are equal in length and bisect each other.
Square: A rectangle with all four sides equal in length. It's also a rhombus with four right angles. Diagonals are equal in length, bisect each other at right angles, and bisect the angles of the square.
Rhombus: A parallelogram with all four sides equal in length. Opposite angles are equal. Diagonals bisect each other at right angles, and bisect the angles of the rhombus.
Trapezium (Trapezoid): A quadrilateral with at least one pair of parallel sides. Note that different definitions exist; sometimes only one pair is required, sometimes exactly one. We'll use the definition requiring at least one pair.
Kite: A quadrilateral with two pairs of adjacent sides that are equal in length. Diagonals intersect at right angles, and one diagonal bisects the other.
Key Properties Summary: | Quadrilateral | Parallel Sides | Equal Sides | Right Angles | Diagonals Equal | Diagonals Bisect Each Other | Diagonals Perpendicular | | :----------- | :------------ | :---------- | :----------- | :------------- | :-------------------------- | :----------------------- | | Parallelogram | 2 pairs | Opposite | 0 | No | Yes | No | | Rectangle | 2 pairs | Opposite | 4 | Yes | Yes | No | | Square | 2 pairs | All | 4 | Yes | Yes | Yes | | Rhombus | 2 pairs | All | Sometimes | No | Yes | Yes | | Trapezium | At least 1 pair| None (general)| Sometimes | No | No | No | | Kite | None | 2 adjacent pairs| Sometimes | No | One bisects the other | Yes | Example 1: Classifying a quadrilateral. Imagine a quadrilateral with all sides equal and with diagonals that bisect each other at right angles. What is it?
Solution: It's a rhombus because all sides are equal and the diagonals bisect each other at right angles. It's also a square because all its angles are right angles. Thus, it's most accurately classified as a square, as a square is a special type of rhombus. 2.2 3D Objects: Cubes and Rectangular Prisms A cube is a 3D object with six square faces. All sides are equal in length. A rectangular prism is a 3D object with six rectangular faces.
Surface Area: The total area of all the faces of the 3D object. Imagine you were wrapping a present; the surface area is the amount of wrapping paper you would need.
Cube: Since all faces are squares and equal, the surface area is 6 (side * side) or 6s², where 's' is the length of one side.
Rectangular Prism: The surface area is 2 (length width + length height + width * height) or 2(lw + lh + wh), where 'l' is length, 'w' is width, and 'h' is height.
Volume: The amount of space a 3D object occupies. Imagine filling a box with sand; the volume is the amount of sand the box can hold.
Cube: Volume is side side * side or s³, where 's' is the length of one side.
Rectangular Prism: Volume is length width * height or lwh, where 'l' is length, 'w' is width, and 'h' is height.
Example 2: Calculating the Surface Area of a Cube A Rubik's Cube has sides of 5.7 cm. What is its surface area?
Solution: Identify the shape: Cube.
Identify the formula: Surface Area = 6s² Substitute the value: Surface Area = 6 * (5.7 cm)² Calculate: Surface Area = 6 * 32.49 cm² = 194.94 cm² Therefore, the surface area of the Rubik's Cube is 194.94 cm².
Example 3: Calculating the Volume of a Rectangular Prism A brick is 22cm long, 11cm wide, and 7cm high. What is its volume?
Solution: Identify the shape: Rectangular Prism.
Identify the formula: Volume = lwh Substitute the values: Volume = 22 cm 11 cm 7 cm Calculate: Volume = 1694 cm³ Therefore, the volume of the brick is 1694 cm³. 2.3 Nets of Cubes and Rectangular Prisms A net is a 2D shape that can be folded to form a 3D object. There are multiple possible nets for a cube and a rectangular prism. The net must have the correct number of faces and they must be arranged so that they can be folded to form the object without overlapping or gaps. Practice drawing nets, cutting them out and folding them to understand how they work. Guided Practice (With Solutions)
Question 1: A square has a perimeter of 36cm. What is the length of each side?
Solution: A square has four equal sides. Perimeter is the sum of all sides.
Therefore, the length of one side is Perimeter /
4. Length of one side = 36 cm / 4 = 9 cm.
Question 2: Calculate the surface area of a rectangular prism with length 8 cm, width 5 cm, and height 3 cm.
Solution: Identify the shape: Rectangular Prism.