![]() In the next example, we’ll continue to use the same formula. So, the area of this trapezoid is 7600 square units. We weren’t given any units in the question, but as this is an area, then we can say that this will be square units or area units. We can then simplify 82 plus 70, giving us 152, and half of 152 is 76. Therefore, we will be calculating one-half times 82 plus 70 times 100. We can recall that the area of a trapezoid is given by a half times □ plus □ times ℎ, where □ and □ are the lengths of the bases and ℎ represents the perpendicular height.įor the given trapezoid, we can substitute 82 and 70 for □ and □, respectively, although it wouldn’t matter if these two values were switched. The height, which will be the perpendicular height, is given as 100 length units. And even though these don’t have units, they would be in length units. We are given the information that the parallel sides or bases of this trapezoid have lengths of 82 and 70. We might choose to begin a question such as this by sketching a trapezoid, recalling that a trapezoid is simply a quadrilateral with one pair of parallel sides. If the height is 100, what is the trapezoid’s area? The parallel sides of a trapezoid have lengths 82 and 70. We’ll now see how we can apply this formula to find the area of a trapezoid given its height and the lengths of its bases. We’re really saying that the area is equal to half the sum of the lengths of the parallel bases multiplied by the height. Notice that this right-hand side is equivalent to calculating □ plus □ times ℎ and dividing by two. But when it comes to finding the area of a trapezoid, don’t worry, we don’t have to always split it into triangles because in fact we have derived a general formula.įormally, we can say that for a trapezoid of perpendicular height ℎ and bases □ and □, the area of a trapezoid is equal to one-half times □ plus □ times ℎ. So, we can think of the area of a trapezoid as half the sum of the parallel bases multiplied by the height. Notice that □ plus □ is the sum of the lengths of the trapezoid’s parallel bases. We can then add these two fractions and take out the common factor of each, which is □ plus □ times ℎ over two. Now, we know that the area of the trapezoid is going to consist of the area of the upper triangle plus the area of the lower triangle. For the lower triangle, its area will be calculated as one-half times □ times ℎ, which is □ℎ over two. So, we’re working out a half times □ times ℎ, which is its perpendicular height. That means then if we consider this upper triangle, the base length of this triangle is □. The area of a triangle is calculated as half times the base times the perpendicular height. We might think about splitting the trapezoid into two triangles because hopefully we recall how to find the area of a triangle. We will now consider how we might find the area of a trapezoid by using these letters □ and □ for the bases of the trapezoid and ℎ for the perpendicular height. Finally, the perpendicular distance between the two bases is the height of the trapezoid, and we usually denote that with the letter ℎ. So, for example, if we were defining an isosceles trapezoid, we could say that the legs are congruent. The two nonparallel sides are called the legs of the trapezoid. When we have a trapezoid, the two parallel sides are usually referred to as the bases, and often they are labeled with the letters □ and □. And if a trapezoid has a right angle, then we can call it a right trapezoid.īefore we see the formula to find the area of a trapezoid, however, let’s see how we can define the different sides in a trapezoid. But of course, by the definition, it doesn’t even need to have these nonparallel sides congruent it just has to have one pair of parallel sides. In fact, both of these would be called an isosceles trapezoid, and they are trapezoids in which the nonparallel sides are of equal length. When we think of a trapezoid, we very typically think of a trapezoid that looks like this first figure or even an upside-down one, like the second figure. But a word of warning, in some parts of the world, you might know this instead as a trapezium, but here we’ll use the term trapezoid. But first, let’s think about exactly what we mean by a trapezoid and the different types of trapezoid that exist.Ī trapezoid is defined as a quadrilateral with one pair of parallel sides. We’ll also see an example of how we can apply these formulas in a real-life context. In this video, we’ll see how we can find the area of a trapezoid using two alternative formulas.
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