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Areas of Trapezoids

Recall that a trapezoid is a quadrilateral defined by one pair of opposite sides that run parallel to each other. These sides are called bases, whereas the opposite sides that intersect (if extended) are called legs. Let’s learn how to measure the areas these figures.

Determining the area of a trapezoid is reliant on two main components of these polygons: their bases and heights. These characteristics helped us find the areas of parallelograms and triangles in the previous section, but there is a slight difference in finding the area of trapezoids: we require the measure of both of its bases. This was not a requirement for parallelograms, and even if it were, we would know their measures since a parallelogram’s bases are congruent.

Let’s begin studying the area of a trapezoid. The area of a trapezoid is equal to one half the height multiplied by the sum of the lengths of the bases. It is expressed as

where A is the area of the trapezoid, h is the height, and b₁ and b₂ are the lengths of the two bases.

The bases and height of the trapezoid are required in order to determine its area.

Let’s work on two exercises that will help us apply this area formula to trapezoids.

Example 1

Find the area of trapezoid ABCD.

Solution:

This problem appears to be quite simple because we are given the lengths of both bases and the height of the trapezoid. It does not matter which base we choose as our first or second base (because addition is commutative). We will just say that b₁ is equal to 10 meters and that b₂ is 18 meters.

The height of our trapezoid is the perpendicular distance between our bases. The illustration shows that this distance is equal to 9 meters. Now that we have the measures of both bases and the height, we can plug them into the area formula for trapezoids. We have

A = 1/2 x 9 x (10 + 18)

A = 1/2 x 9 x 28 = 14 x 9 = 126

Therefore Area = 126m²

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