Area of a General Polygon

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    • Area of an Irregular Polygon
    • Summary
    • What’s Next?

    In the previous segment, we learnt about the area of a trapezium. In this segment, we will learn how to find the area of a general polygon.

    How to find the are of an irregular polygon?

    We know that a polygon is a simple closed figure made up of only line segments. Based on the number of sides, a polygon is named a triangle, a quadrilateral, pentagon, hexagon and so on.

    We have seen how to find the areas of a triangle and quadrilaterals like square and rectangle. We will now learn how to find the area of any polygon with help of a general quadrilateral.

    Consider the quadrilateral ABCD.

    Quadrilateral ABCD

    Joining the opposite vertices A and C divides the quadrilateral into 2 triangles. Hence, Area (quadrilateral ABCD) = Area (triangle ABC) + Area (triangle ADC)

    Area of quadrilateral ABCD

    Formula for area of a triangle = ½ x base x height

    AC is the common base for both triangles. Dropping perpendiculars BX and DY on to AC gives us the heights of triangles ABC and ADC respectively.

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