List the vertices in order around the polygon and repeat the first vertex at the end. \(A=\dfrac12\l

Question

List the vertices in order around the polygon and repeat the first vertex at the end.

$A=\dfrac12\left|x_1y_2+x_2y_3+x_3y_1-x_2y_1-x_3y_2-x_1y_3\right|$

For a triangle, use the formula above. Extend the same pattern to more vertices. The absolute value makes the area positive for either orientation.

Example: $(1,2),(5,0),(3,6)$

Special quadrilaterals

Property	True for
Diagonals bisect each other (share the same midpoint)
Diagonals are perpendicular to each other
Opposite sides are equal and parallel

Use equal diagonal midpoints to test bisection, and perpendicular gradients to test right angles.

Accepted Answer

The triangle has area $10\text{ units}^2$. Diagonals bisect each other for parallelograms, rhombuses, rectangles and squares; they are perpendicular for kites, rhombuses and squares; opposite sides are equal and parallel for parallelograms, rhombuses, rectangles and squares.

Areas of Polygons and Special Quadrilaterals

Areas of Polygons and Special Quadrilaterals

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