2D & 3D GEOMETRY (Area & Volume) Using Visual Tools

Learn how to compute perimeter as the total boundary length and area as the surface inside figures, using real-life examples and the square-counting method to practice diverse problems.

Learn how to calculate the perimeter of triangles, rectangles, and squares by summing boundary lengths, with examples using Pythagoras for missing sides and a complex figure.

Compute the area of rectangles by multiplying length and width, analyze single and composite shapes, and apply perimeter calculations to understand surface and boundary in centimetres.

Discover how to compute the area of a parallelogram by base times height, using any side as base and the perpendicular distance as height.

Compute triangle area using half base times height, relate it to parallelogram area, apply Heron's formula, use sides with included angle and equilateral formula root three by four a square.

See how a trapezium, a quadrilateral with two parallel sides, decomposes into a parallelogram and a triangle; compute area using h/2 (a+c) or by summing parts.

Divide the quadrilateral along its diagonal into two triangles, compute each area as one-half times the diagonal times its height (h1 and h2), then sum them.

Explore circumference and area of circles, including sectors and segments, using pi, radius, and diameter; apply 2 pi r, pi r squared, and sector/arc formulas.

Explore area and perimeter problems across squares, rectangles, triangles, circles, and semicircles using visual reasoning and core formulas. Build skills in area, perimeter, diagonals, altitudes, and circle sectors.

Visualize area and perimeter problems with squares, rectangles, rhombuses, circles, and triangles; apply Pythagoras and diagonal properties to compute areas, perimeters, and related measurements.

Explore area and perimeter problems using circle sector formulas, unitary methods, and hexagon and triangle geometry, including shaded region calculations and equilateral triangle properties.

Explore 3d shapes, surface area and volume, grounded in 2d shapes like circle and rectangle, and learn about cuboid, slender cone, pyramid, sphere, cube, cylinder, and prism.

Explains cuboids and cubes by deriving surface area, little surface area, and volume from length, width, and height, and introduces face and body diagonals via Pythagoras.

Explore the right circular cylinder, its circular bases and curved surface, and derive surface area and volume using r and height, with practical examples like hollow cylinders.

Study right circular cones: radius r, height h, slant height l with l^2 = h^2 + r^2. Calculate lateral surface area π r l and volume (1/3) π r^2 h.

This lecture introduces the sphere and hemisphere, defines radius and diameter, and presents surface area and volume formulas, including sphere 4πr^2 and 4/3πr^3, and hemisphere 2/3πr^3 with two surface components.

Review the formulas for surface area and volume of cuboids, cubes, cylinders, cones, spheres, and hemispheres, including total surface areas, curved surfaces, and bases.

Explore computing the volume and surface area of combined solids, such as hemispheres with a cylinder or a cone with a hemisphere, using fundamental surface-area techniques.

Explore prisms and pyramids: prisms have two congruent bases, pyramids have one; volume is base area times height for prisms and one third that for pyramids.

Tackle problems on 3d solids, from hemisphere–cube composites to cylinders, cones, and spheres, using surface area and volume calculations, ratios, and melting into new shapes.

Celebrate completing the course on 2d and 3d geometry using visual tools, mastering area and volume through creative animation.