To) than the area of the **trapezium** Kabl by two-thirds of the area of the triangle ATB (§ 34).

In shape, the peninsula forms a rough **trapezium**, with its greatest length from north-west to south-east.

The " **trapezium** " of stars in the Orion nebula.

- In § 23 the area of a right **trapezium** has been expressed in terms of the base and the two sides; and in § 34 the area of a somewhat similar figure, the top having been replaced by an arc of a parabola, has been expressed in terms of its base and of three lengths which may be regarded as the sides of two separate figures of which it is composed.

The most important form of **trapezium** is that in which one of the two remaining sides of the figure is at right angles to the two parallel sides.

Angle of an irregular **trapezium** of land which lay between the rivers Husur (Khausar, Choser) on the N.W., Gomal on the N.E.

The figures considered in § 22 are particular cases of the **trapezium**, which is a quadrilateral with two parallel sides.

1) be a **trapezium**, the sides CA and DB being parallel.

Then MA'B'N is a right **trapezium**, whose area is equal to that of Cabd; and it is related to the latter in such a way that, if any two lines parallel to AC and BD meet AB, CD, MN, A'B', in E, G, P, E', and F, H, Q, F', respectively, the area of the piece PE'F'Q of the right **trapezium** 'B.

This formula holds for the general case in which the base is a **trapezium**; the wedge being thus formed by cutting a triangular prism by any two planes.

The trapezette is then a right **trapezium**, and its area, if m=l, is 2h(uo + ui) or hug.

The **trapezium** is a particular case.

Hence the areas of the trapezette and of the **trapezium** will be equal if I - 2=3,0=I/%/3.

The **trapezium** is also sometimes called a " trapezoid," but it will be convenient to reserve this term for a different figure (§ 24).

The right **trapezium** so constructed, F ' may be called the equivalent right **trapezium**.

In E'; the case of a parallelogram, the equivalent right,, **trapezium** is a rectangle; in the case of a triangle, Al it is a right-angled triangle.

If, for instance, the graph were a **trapezium**, the calculation of the area would be equivalent to finding the integral, from x=a to x=b, of an expression of the form px+q.

Hence the area of the right **trapezium** Khjl is greater than the area of the trapezette Kacbl.