0Heron’s Formula (Conceptual)
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Used to find the area of a triangle when you know the lengths of all three sides.
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Instead of measuring height, you can calculate area directly from the sides.
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Helpful for scalene triangles, where no side is equal and height is hard to measure.
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Key Idea: First, understand the semi-perimeter (half the sum of all sides). The area depends on this and the three sides.
Important Notes:
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Works for all types of triangles: equilateral, isosceles, scalene.
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Saves time when height is unknown.
2. Surface Areas (Conceptual)
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Surface area is the total area that covers the outside of a 3D object.
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It tells us how much material is needed to cover the shape.
Common 3D Shapes:
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Cube – 6 equal square faces
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Cuboid (Rectangular Box) – 6 rectangular faces
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Sphere – perfectly round 3D object
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Cylinder – circular top and bottom with a curved surface
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Cone – circular base and pointed top
Key Notes:
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Total surface area = sum of areas of all faces and curved surfaces
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Helps in painting, wrapping, or covering objects
3. Volumes (Conceptual)
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Volume is the space occupied by a 3D object.
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It tells us how much material the shape can hold.
Common 3D Shapes:
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Cube – volume = space inside a cube
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Cuboid – volume = space inside a box
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Sphere – volume = space inside the ball
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Cylinder – volume = space inside a can
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Cone – volume = space inside a cone-shaped object
Key Notes:
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Volume is measured in cubic units (like cubic meters, cubic cm).
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Useful for containers, tanks, and solids.
4. Important Points for Exams
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Heron’s formula: area of triangle using all 3 sides; works for all triangles.
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Surface area: total area covering the outside of a 3D object.
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Volume: total space inside a 3D object.
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Common 3D shapes to remember: cube, cuboid, sphere, cylinder, cone.
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Surface area → useful for covering/wrapping.
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Volume → useful for filling/holding.
