Substituting the known area of the trapezoid ( 4 500 m 2) and the known height We are given the height of the trapezoid ( 25 m) and we now know that its area, which is the same as the areaĪs we wish to calculate the length of the middle base of the trapezoid, we recall the formula for the area of a trapezoid that involves this measure:Ī r e a o f t r a p e z o i d l e n g t h o f m i d d l e b a s e h e i g h t = ×. This field is in the shape of a trapezoid because it is a quadrilateral with one pair of parallel sides. Next, we consider the field on the right in the figure. Hence, we haveĪ r e a o f r h o m b u s m = 1 0 0 × 9 0 2 = 9 0 0 0 2 = 4 5 0 0. Where □ and □ represent the lengths of its diagonals. We then recall that the area of a rhombus is given byĪ r e a o f r h o m b u s = □ □ 2, We are given the lengths of the rhombus’s two diagonals: they are 100 m andĩ0 m. This is the field in the shape of a rhombus because its four side lengths are all equal. We begin by considering the field on the left in the figure. “half the sum of the parallel bases, multiplied by the height.” In fact, “half the sum of the parallel bases” has a geometric significance, Informally, we said this formula can be thought of as We now consider an alternative way of specifying the formula for the area of a trapezoid. Hence, the length of the other parallel side (or base) of the trapezoid is 49 units. We begin by simplifying the right-hand side of the equation by canceling out a factor of 2:ĭividing both sides of the equation by 20 givesįinally, subtracting 39 from each side of the equation gives Substituting each of these values into the formulaĪbove gives an equation we can solve to determine the length of the other parallel side: Of the trapezoid, is 40 units and the length of one parallel side, or base, of the trapezoid is 39 units. The distance between the parallel sides, which is another way of saying the height We are given that this trapezoid has an area of 1 760 square units. We recall that the area of a trapezoid with parallel sides (or bases) of lengths □ and □ unitsĪ r e a o f t r a p e z o i d = 1 2 ( □ + □ ) ℎ. ![]() If one parallel side is 39, what is the other side? Answer In our next example, we will consider how to find the length of one of the parallel sides of a trapezoid given its area, its height,Īnd the length of the other parallel side.Įxample 3: Finding the Length of a Base of a Trapezoid given Its AreaĪ trapezoid has area 1 760 and the distance between its parallel sides is 40. Worded description are important skills when answering geometric problems. Understanding the measurements needed to apply a particular formula and being able to select the relevant information from a diagram or The length of the leg of the trapezoid was not required in order In the example we have just seen, we were given more information than we needed in the figure. Hence, the height of the trapezoid is 160 yd. Multiplying both sides of the equation by 2 3 7 5 (the multiplicative inverse of 3 7 5 2) gives We now solve this equation to determine the value of ℎ. ![]() Represents the unknown height of the trapezoid: We can use the given area of the trapezoid and the lengths of the two parallel bases to form an equation where ℎ ![]() ( 232 yd), but this is not relevant to our calculation, as it is not the perpendicular height of the trapezoid. We have also been given the length of one leg of the trapezoid We begin by recalling that the area of a trapezoid can be calculated by multiplying half the sum of the lengths of the parallel bases by the perpendicular height.įrom the figure, we identify that the parallel bases of the trapezoid have lengths 80 yd andĢ95 yd.
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