Firstly, note how we require here only one of the legs to satisfy this condition – the other may or may not. Secondly, observe that if a leg is perpendicular to one of the bases, then it is automatically perpendicular to the other as well since the two are parallel. With these special cases in mind, a keen eye might observe that rectangles satisfy conditions 2 and 3. Indeed, if someone didn't know what a rectangle is, we could just say that it's an isosceles trapezoid which is also a right trapezoid. Quite a fancy definition compared to the usual one, but it sure makes us sound sophisticated, don't you think?īefore we move on to the next section, let us mention two more line segments that all trapezoids have. The height of a trapezoid is the distance between the bases, i.e., the length of a line connecting the two, which is perpendicular to both. In fact, this value is crucial when we discuss how to calculate the area of a trapezoid and therefore gets its own dedicated section. The median of a trapezoid is the line connecting the midpoints of the legs. In other words, with the above picture in mind, it's the line cutting the trapezoid horizontally in half. It is always parallel to the bases, and with notation as in the figure, we have m e d i a n = ( a + b ) / 2 \mathrm \times h A = median × h to find A A A.Īlright, we've learned how to calculate the area of a trapezoid, and it all seems simple if they give us all the data on a plate. But what if they don't? The bases are reasonably straightforward, but what about h h h? Well, it's time to see how to find the height of a trapezoid. Let's draw a line from one of the top vertices that falls on the bottom base a a a at an angle of 90 ° 90\degree 90°. (Observe how for obtuse trapezoids like the one in the right picture above the height h h h falls outside of the shape, i.e., on the line containing a a a rather than a a a itself. Nevertheless, what we describe further down still holds for such quadrangles.) The length of this line is equal to the height of our trapezoid, so exactly what we seek. Therefore, the weight of the water is 0.56 metric ton.Note that by the way we drew the line, it forms a right triangle with one of the legs c c c or d d d (depending on which top vertex we chose). W e i g h t = V o l u m e × De n s i t y = 0.56 m 3 × 1 metric ton/m 3 = 0.56 metric ton Since the density of water is approximately 1 metric ton/m^3, the weight of the water will be: The problem states that the trough is filled with water. Therefore, the volume of the trough is 0.56 m^3. Substituting the values from the problem into the formula above, the volume (in meter cube) of the trough can be calculated as follows: The formula for the volume of a right trapezoidal prism is given by: The height of the trapezoidal tank (h) is 200 cm.The length of the top of trapezoid(b) is 40 cm.The length of the base of trapezoid(a) is 100 cm.The dimensions of the trough are not specified in the solution but mentioned in the question. Identify the given parameters and formula for the volume of a trapezoidal prism.Ī drinking trough for horses is a right trapezoidal prism.
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