Trapezoid Formula

How to Find the Height of Trapezium?

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

H= Height

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

Where,

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

Example:

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.

Solution:

Area = = (a + b)/2 × h

Area = ½ (26+12) × 6

Area = ½ (38) × 6

Area= 114 sq.inch

FAQs (Frequently Asked Questions)

Q1. What is a Trapezoid?

Answer: In geometry, A trapezoid is a quadrilateral having one pair of parallel sides. Therefore, this 4-sided polygon makes for a closed object and a plane figure. It consists of four-line segments in addition to four interior angles. The parallel sides are actually the trapezoid's two bases; while the other two sides are its legs.

Q2. What is the Height of the Trapezoid?

Answer: The bases are the 2 parallel sides of the trapezoid. The height or (altitude) of a trapezoid also known as the trapezium is the perpendicular distance between the two bases.

Q3. How to Find the Height of Trapezium Given the Area?

Answer: We can find the height (altitude) of a trapezoid given the two bases and the area. The main area formula of the trapezoid or (trapezium) has four variables (area, two bases and altitude). Remember that if we are familiar with any three we can always find the fourth. So for example, if we know the two bases and the area we can calculate the height, simply by rearranging the main formula:


Height (altitude) = 2a / b1+b2 

Where,

a = The area

b1 and b2 = The two bases.