To find the height of a trapezoid, we can also find the area of any trapezoid, beginning by labelling its bases and altitude. In a trapezoid, mark the longer base ‘a’ and the shorter base ‘b’. Mark a line perpendicular to the two bases h for height or altitude of a trapezoid. The area of the trapezoid is the average of the bases multiplied by the altitude. Where,
A = Long Base
B= Short Base
Area = (a + b)/2 × h
Note: We are not required to know anything about the length of the legs or the angles of the vertices to determine the area.
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Trapezium Height Formula
Height of trapezium formula : h = 2 A / a+b
A = Area of the Trapezoid
a = Base
b = Base
How Do You Find The Height of a Trapezium?
Because the legs (non-parallel sides) of the trapezoid are equivalent, the height of the trapezoid can be computed as given. To obtain the two triangles' bases, we need to subtract the two bases. Suppose that the measure is 10 cm and 5 cm. Now we need to subtract 5cm from 10cm and divide by 2. 102 = h2 + 52 using the Pythagorean Theorem, the height (h) is calculated as; 100 = h2 + 25. Thus, h2 = 75
How to Find the Height of Trapezium Using Area of Triangle
We can also find the height of the trapezoid by using the Area of a Triangle Formula and Heron's Formula. For that, we need to divide the trapezium into a triangle and a parallelogram. Now, find the area of the triangle applying the properties of the parallelogram and heron's formula. Insert the values of the area of the triangle into the equation 1/2 × b × h. Since b is known, it is very simple to find H.
Moreover, if the trapezoid is an isosceles trapezium there is a direct formula for calculating the height i.e. √(Eq. side) 2 - (1/2 × base) 2
Solved Examples Using Trapezoid Formula
A trapezoid is upside down from how you generally observe them, but don't let that stop you! The short base is 12 inches long. The long base a (this time at the top of the trapezoid) is 26 inches long. The altitude or height h (irrespective of which way you see the trapezoid) is 6 inches. Find the area of the trapezoid.
Area = = (a + b)/2 × h
Area = ½ (26+12) × 6
Area = ½ (38) × 6
Area= 114 sq.inch