Quadrilaterals
A quadrilateral is a closed 2-D figure with four straight sides ("quad" means four and "lateral" means side).
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Some properties of quadrilaterals have are:
There are a few special quadrilaterals with specific names based on their properties:
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Tip: Based on their properties, all rectangles, squares, and rhombuses are parallelograms, but not all parallelograms are rectangles/squares/rhombuses! Similar idea occurs with rectangles and squares - all squares are rectangles, but not all rectangles are squares.
Triangles
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When the base and height of a triangle are given, the area is calculated as: \(Area=\frac{1}{2} \times base \times height\) \(=\frac{1}{2}bh\)
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When all the side lengths of the triangle are given, the area is calculated using Heron's Formula: \(Area=\sqrt{s(s-a)(s-b)(s-c)}\), where \(s=\frac{1}{2}(a+b+c)\)
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Circles
| Arc | Any connected part between two points on a circle. |
| Chord | A line segment whose endpoints lie on the circle (divides a circle into two segments). |
| Radius | The straight-line segment that connects a centre of the circle to a point on a circle. |
| Sector | A figure formed by two radii and an arc (determined by the endpoints of the radii). |
| Segment | A figure formed by an arc and chord joining the endpoints of the arc. |
| Vertex (Vertices) | A point where two or more line segments meet (i.e. a corner). |
| Edge (Edges) | A line segment joining one vertex/corner to another or a line segment where two faces meet. |
| Face (Faces) | Any individual flat surface of a 3D figure. |
| Surface Area | Total area of the surfaces of a 3D figure. |
| Lateral Area | Surface area of a 3D figure, excluding its base and top (when they exist). |
| Volume | The amount of 3D space that is occupied/taken up by a 3D figure. |
Example 1
