Before you find the area of a trapezoid, you must give it definition.
Trapeze - a geometric shape with four corners at which two sides are parallel to each other, and the other two - no.The two sides that are parallel to each other, called bases, and non-parallel - side.If the parties, which are lateral, equal, an isosceles trapezoid will be called.If the intersection they form a right angle, it is rectangular.
In algebra, there is the concept of a curvilinear trapezoid - It is understood as a figure, bounded on one side of the x-axis, and the other - the graph of y = f (x) b and is defined on the interval [a;b]
How to find the area of a trapezoid
calculated such geometrical figure by the formula S = 0,5 * (a + b) * h, where A and B are the length of the base of the trapezoid, and h - its height.
example.Dana trapezoid, the base of which one is 2 cm, the second - 3 cm, height - 4 cm. We expect the area under the formula, we get the result: S = 0, * 5 (2 + 3) * 4 = 12 cm2.
From the same formula that, knowing the area of the figure, its height, the length of one side, you can find the length of the other.The second option - knowing the lengths of the sides and the area of a trapezoid, you can find her height.
example.Dana Keystone, which has one base longer than the other 3 times.The height of figures - 3 cm, the area - 24sm2.Required to find the length of both bases.
decision.The area is calculated using the following formula S = 0.5 * (a + b) * h.Because of the problem is clear that one side more than the other 3 times, hence a = 3b.Replace in the formula and obtain S = 0.5 * (a + 3b) * h = 0.5 * 4B * h.As a result, we obtain S = 2c * h, i.e. a = S / 2h.Substitute numerical values and get in = 6 cm, a = 18 cm.
However, this is not the only way that you can determine the area of this figure.In the second method, before you find the area of a trapezoid, it can be divided into simple geometric shapes: rectangle and two triangles (or a triangle, in the case of a rectangular trapezoid).In this case, the total area is calculated as the sum of the areas of these figures.As an option - you can insert it into a rectangle side of which will be equal to the length of the larger bases.In this case, the area of the trapezoid is determined as the difference squares rectangles and triangles.
How to find the area of a rectangular trapezoid?We have already mentioned that the rectangular trapezoid can be called a trapezoid, whose base (call it a) and side to intersect, forming a prima corner.Accordingly, in the above figure with avsd side will be high.Then, knowing the length of all three sides, you can find the area of shapes S = 0,5 * (a + b) * c.
The simplest formula is as follows: S = a * h, where k - is the length of the midline of the trapezoid, h - its height.The problem is that in practice it is easier to measure the length of the base than to find the midline.And it is as follows:
Given: scalene, trapezoid AVSD non-rectangular, in which the sides AB and CD are the bases.Before you find the area of a trapezoid, the next leg of the AU and the VD divided into 2 equal parts, marking the point of intersection of the letters T and C. Then the line GK, held parallel to the ground, and will be the middle line of the trapezoid m.
Another special case - where equilateral trapezoid.For it fit all of the formula (of course, except for a rectangular formulas).Its area can be determined by knowing the angle between the bases.The formula is as follows: S = (a + b) * c * sin (x) * 0.5, where A and B - the length of base side length c and x - the angle between them.
sometimes necessary to determine the area of this figure has not only the geometry, but in algebra on the coordinate system.In this regard, students have the question of how to find the area of a trapezoid in the coordinates.The principle of computation is the same - determines the length of the sides, as the difference of coordinates of points base height is calculated and the first formula is calculated area.The height will be considered a line drawn from the corner of one of the grounds to another base.
to determine the area of a curvilinear trapezoid are integral.
