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 And since it is, then our answer runs up to 83.14 square centimetres for the area of □□□□.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. And now to find the answer to two decimal places, we check the third decimal digit to see if it is five or more. We get an answer of 83.138438 and so on square centimetres. So we can go ahead and use our calculator to simplify our answer. Notice, in the question that we were asked for value to two decimal places. And we could simplify our 24 over two as 12. Substituting our values, we have eight plus 16 over two times root 48. We can now work at the area of our trapezoid using the formula. We leave our answer in this root form, since we’re not finished using this value of each in our calculations. And finally, to find ℎ then, we take the square root of both sides, giving us that ℎ is equal to root 48. To find ℎ squared by itself, we subtract 16 from both sides. Substituting our values will give us eight squared equals eight squared plus four squared, where ℎ is, of course, the height of the triangle and not the hypotenuse. ![]() We can use the Pythagorean theorem here which says that the square of the hypotenuse is equal to the sum of the squares on the other two sides. If we take a closer look at one of the triangles in our trapezoid, we have a hypotenuse of eight centimetres and two other lengths. Therefore, we must have four centimetres, eight centimetres, and four centimetres. And we know that these three lengths will add up to 16 centimetres. We know that the basis of the two triangles will be the same length, since we have an isosceles trapezoid. To find the length of the base of this triangle, we can notice that, on the line □□, we have an eight-centimetre segment. But it will be possible to work this out if we know the base of the triangle and we use the Pythagorean theorem. Looking at our diagram, however, we can see that we’re not told the perpendicular height. To find the area of the trapezoid, we use the formula that the area of a trapezoid is equal to □ plus □ over two times ℎ, where □ and □ are the basis and ℎ is the perpendicular height. An isosceles trapezoid has one pair of nonparallel sides congruent. We can notice that our lengths □□ and □□ are the same, which is why we’re told that it is an isosceles trapezoid. ![]() In a trapezoid, we will have a pair of parallel sides. □□ □□, and □□ are all eight centimetres. We’re told that there are three equal sides. And in the rest of the world, this will be a trapezium. In the US and Canada, you know this as a trapezoid. So in the diagram, we have our trapezoid □□□□ and just a quick word about the naming of this shape. Find the area giving the answer to two decimal places. □□□□ is an isosceles trapezoid where □□ equals □□ equals □□ equals eight centimetres and □□ equals 16 centimetres.
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