Volume and Surface Area of Pyramids, Cones, Spheres
? Video Tutorial Volume of Pyramids and Cones: $frac{1}{3} times text{base area} times text{height}$, where height is always perpendicular to the base. Surface Area of Pyramids: Add the base area and the areas of all triangular sides. Surface Area of Cones: Add the base circle area $(pi times r^2)$ and the lateral surface area ($pi […]
Perimeter of a Polygon
? Video Tutorial Perimeter of a Polygon: The total length around a polygon. Add up the lengths of all sides to find the perimeter. Perimeter Formulas: For rectangles, use $2 times (text{length} + text{width})$. For squares, the perimeter is $4 times text{side length}$. Triangle Perimeter: For a general triangle, add all three sides. For isosceles […]
Area of Parallelograms and Triangles
? Video Tutorial Height of Parallelogram: The height ($h$) is always perpendicular to the base and may lie inside or outside the parallelogram. Area of a Parallelogram: The formula is $A = b times h$, where $b$ is the base and $h$ is the perpendicular height. Height of Triangle: Like in a parallelogram, the triangle’s […]
Volume of a Cuboid and Cube
? Video Tutorial Volume of a Cuboid: $text{V} = text{length} times text{width} times text{height}$ Volume of a Cube: $text{V} = text{side}^3$ Finding Missing Dimensions: If the volume and two dimensions of a cuboid are known, you can rearrange the volume formula to find the missing dimension. Volume of Complex Shapes: Can be broken down into […]
Surface Area of Solids
? Video Tutorial Surface Area of a Cuboid: Calculate each pair of faces (top-bottom, front-back, left-right) and sum their areas to find the total surface area. Surface Area of a Cube: Since all 6 faces of a cube are identical squares, the surface area formula is $6 times text{side}^2$. Surface Area of a Triangular Prism: […]
Volume of Prisms and Cylinders
? Video Tutorial Volume Formula for Prisms and Cylinders: $V = B times h$, where $B$ is the area of the base and $h$ is the height. For Prisms: First calculate the area of the base shape, such as a triangle or rectangle. For Cylinders: The base of a cylinder is a circle, so use […]
Cavalieri’s Principle
? Video Tutorial Cavalieri’s Principle for Volume: If two solids have the same height and identical cross-sectional areas, they have the same volume, even if they look different. Simple Volume Calculation: Use Cavalieri’s principle to find the volume of an inclined shape by calculating its upright equivalent’s volume with formula $text{base area} times text{height}$. ? […]
Constructing Triangles
? Video Tutorial Triangle Basics: Triangles consist of vertices, sides, and angles, labelled in a specific way. Angle-Side-Angle (ASA) Construction: Start with the known side, then use a protractor to draw the two angles at each end. Where lines intersect is the third vertex. Side-Side-Angle (SSA) Construction: Be careful, this may create two possible triangles. […]
Congruent Triangles
? Video Tutorial Congruent Triangles: Have identical side lengths and angle measures, meaning they match in size and shape. Side-Side-Side (SSS): If all three sides of two triangles are equal, the triangles are congruent. Side-Angle-Side (SAS): Two triangles are congruent if they share two equal sides and the angle between them. Angle-Side-Angle (ASA): Two triangles […]
Thales’ Theorem
? Video Tutorial Thales’s Theorem: A triangle formed by a circle’s diameter and any point on the semicircle is always a right-angled triangle (the angle opposite this diameter is $90^circ$). Sum of interior angles in triangles: Remember, the sum of interior angles in any triangle is always $180^circ$, allowing you to solve for unknown angles […]