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Chapter 9: Area of Plane Figures

    Introduction

    Area of a Trapezium

    Area of a Quadrilateral

    Area of a Rhombus

    Surveying the Field

    Area of a Polygon

    Area of a Circle

    Area of a Circular Path or Area of a Ring

    Length of the Arc

    Area of Sector

    Exercise 9.1

    Exercise 9.2

    What We Have Discussed?

    Easy Level Worksheet

    Moderate Level Worksheet

    Hard Level Worksheet

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Chapter 9: Area of Plane Figures > Area of a Trapezium

Area of a Trapezium

Recall that trapeziums are quadrilaterals with one pair of parallel sides. These parallel sides are called the bases of the trapezium.

Like before, try to draw a rectangle that has the same area as this trapezium. Can you see how the missing and added triangles on the left and the right cancel out?

The height of this rectangle is the the parallel sides of the trapezium.

The width of the rectangle is the distance between the of the two non-parallel sides of the trapezium. This is called the midsegment of the trapezium.

Like with triangles, the midsegment of a trapezium is its two bases. The length of the midsegment is the average of the lengths of the bases: a+c2.

If we combine all of this, we get an equation for the area of a trapezium with parallel sides a and c, and height h:

A=h×a+c2