Shape Properties: – Recognising and describing 2D shapes and 3D solids.

SHAPE PROPERTIES Recognising and describing 2D shapes and 3D solids. Grade 7 Mathematics: Shape Properties – Recognising and Describing 2D Shapes and 3D Solids Subtopic Navigator Introduction Polygons and Basic 2D Shapes Circles and Their Properties 3D Solids and Their Features Nets of Solids Applications and Mixed Problems Cumulative Exercises Conclusion Lesson Objectives Identify and classify common 2D shapes based on sides and angles. Recognise and describe properties of circles including radius, diameter, and circumference. Describe 3D solids using terms like faces, edges, and vertices. Relate nets of solids to their 3D forms. Lesson Introduction Shapes are everywhere — in buildings, art, nature, and technology. In mathematics, we study 2D shapes (flat figures such as triangles and circles) and 3D solids (solid objects such as cubes and spheres). Recognising and describing their properties helps us solve geometry problems and apply knowledge in fields like engineering, architecture, and design. Polygons and Basic 2D Shapes A polygon is a closed 2D shape formed by straight lines. Polygons are named by their number of sides: triangle (3), quadrilateral (4), pentagon (5), hexagon (6), etc. Key properties include sides, angles, and symmetry. [Insert diagram of different polygons: triangle, square, pentagon, hexagon] Example 1: A polygon has 8 equal sides and 8 equal angles. What type of polygon is it? Solution: A polygon with 8 equal sides and angles is called a regular octagon. Each interior angle can be found using: [latex]frac{(n - 2) times 180^circ}{n} = frac{(8 - 2) times 180}{8} = 135^circ[/latex]. Thus, each angle measures 135°. Exercises (Polygons) Classify a polygon with 12 equal sides. Find each interior angle of a regular hexagon. Circles and Their Properties A circle is the set of all points equidistant from a fixed point (the centre). Important parts: radius, diameter, circumference, and chord. [Insert diagram of a circle showing radius, diameter, chord, and arc] Example 2: A circle has a radius of 7 cm. Find its circumference. Solution: Circumference is given by [latex]C = 2 pi r[/latex]. Substituting: [latex]C = 2 times 3.142 times 7 = 43.994 approx 44 text{ cm}[/latex]. Exercises (Circles) Find the diameter of a circle with radius 15 cm. Calculate the area of a circle with diameter 20 cm. 3D Solids and Their Features 3D solids have faces (flat surfaces), edges (where two faces meet), and vertices (corners). Examples include cubes, cuboids, cylinders, cones, spheres, and pyramids. [Insert diagram showing cube, cone, cylinder, pyramid, and sphere] Example 3: A cube has how many faces, edges, and vertices? Solution: A cube has 6 square faces, 12 edges, and 8 vertices. Exercises (3D Solids) How many faces does a triangular prism have? List the edges and vertices of a square pyramid. Nets of Solids A net is a 2D pattern that can be folded to form a 3D solid. Nets help us understand surface areas of solids. [Insert diagram of cube net and pyramid net] Example 4: The net of a cube is made up of how many squares? Solution: A cube has 6 square faces, so its net is made up of 6 equal squares. Exercises (Nets) Sketch a net for a triangular prism. How many faces will you find in the net of a cuboid? Applications and Mixed Problems Example 5: A cylindrical water tank has a radius of 3.5 m and height 10 m. Find its curved surface area. Solution: Curved surface area = [latex]2 pi r h = 2 times 3.142 times 3.5 times 10 = 219.94 , text{m}^2[/latex]. Exercises (Applications) A cube has side 8 cm. Find its surface area. A cone has height 12 cm and radius 5 cm. Find its slant height using Pythagoras’ theorem. Cumulative Exercises Find each interior angle of a regular decagon. A circle has circumference 62.8 cm. Find its radius. State the number of faces, edges, and vertices of a cuboid. Sketch the net of a square-based pyramid. A cylinder has diameter 14 cm and height 20 cm. Find its volume. Find the area of a semicircle with radius 10 cm. Which solid has one curved surface and two flat circular faces? A prism has 5-sided bases. What is its name? Find the total surface area of a cube of side 5 cm. Explain why all cubes are cuboids but not all cuboids are cubes. Conclusion/Recap In this lesson, we studied 2D polygons, circles, and 3D solids with their nets. Understanding properties of shapes is essential for geometry, measurement, and real-world problem solving. Mastery of these ideas supports advanced topics like mensuration and coordinate geometry. Clip It! Share your ANSWER in the Chat. Indicate TITLE e.g Linear Equation 1. .....2. e.t.c