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Area Of Trapezium – Definition, Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Area of TrapeziumArea Of Trapezium – Definition, ExamplesTable of ContentsArea of Trapezium Definition of Area of Trapezium

A trapezium is a quadrilateral with exactly one pair of parallel sides. The area of a trapezium is the region covered by a trapezium in a 2D plane, measured in square units. The two parallel sides of a trapezium are called bases, while the non-parallel sides are referred to as legs. The perpendicular distance between the two parallel sides is known as the height or altitude of the trapezium. The area of a trapezium can be calculated using the formula: Area of Trapezium=12×Sum of parallel sides×height\text{Area of Trapezium} = \frac{1}{2} \times \text{Sum of parallel sides} \times \text{height}Area of Trapezium=21​×Sum of parallel sides×height or Area=12×(a+b)×h\text{Area} = \frac{1}{2} \times (a + b) \times hArea=21​×(a+b)×h where aaa and bbb are the lengths of parallel sides, and hhh is the height.

There are different types of trapeziums based on their properties. If the non-parallel sides (legs) of a trapezium are equal in length, it is called an isosceles trapezium. When all sides and angles of a trapezium have different measurements, it is known as a scalene trapezium. The line segment connecting the midpoints of the non-parallel sides of a trapezium is called the mid-segment, which is parallel to the bases. It's worth noting that different regions have varying definitions of trapezium and trapezoid, with some definitions considering a parallelogram as a special type of trapezium.

Area of Trapezium

Examples of Area of Trapezium Example 1: Finding the Area of a Trapezium with Known Dimensions Problem:

A trapezium has base lengths a = 222222 inches and b = 262626 inches respectively. The distance between them is 181818 inches. Find the area of trapezium.

trapezium

Step-by-step solution:

Step 1, Write down the given information. We have base lengths a = 222222 inches and b = 262626 inches, and height h = 181818 inches.

Step 2, Use the area formula for a trapezium. The formula is Area=12×(a+b)×h\text{Area} = \frac{1}{2} \times (a + b) \times hArea=21​×(a+b)×h

Step 3, Substitute the values into the formula.

Area=12×(22+26)×18\text{Area} = \frac{1}{2} \times (22 + 26) \times 18Area=21​×(22+26)×18

Step 4, Calculate the sum of the parallel sides.

22+26=4822 + 26 = 4822+26=48 inches

Step 5, Multiply the sum by the height and divide by 222.

Area=12×48×18=432\text{Area} = \frac{1}{2} \times 48 \times 18 = 432Area=21​×48×18=432 inches²

Step 6, Write the final answer. The area of the trapezium is 432432432 square inches.

Example 2: Finding the Missing Side of a Trapezium Problem:

The area of a trapezium is 352352352 feet², the height is 161616 feet, and one of the parallel sides is 252525 feet. Find the length of the other parallel side.

trapezium

Step-by-step solution:

Step 1, List what we know and what we need to find. We know the area is 352352352 feet², height h = 161616 feet, and one side b = 252525 feet. We need to find the other parallel side a.

Step 2, Use the area formula and substitute the known values.

Area=12×(a+b)×h\text{Area} = \frac{1}{2} \times (a + b) \times hArea=21​×(a+b)×h 352=12×(a+25)×16352 = \frac{1}{2} \times (a + 25) \times 16352=21​×(a+25)×16

Step 3, Solve for a by first multiplying both sides of the equation by 2.

352×2=(a+25)×16352 \times 2 = (a + 25) \times 16352×2=(a+25)×16 704=(a+25)×16704 = (a + 25) \times 16704=(a+25)×16

Step 4, Divide both sides by 161616 to isolate (a + 252525).

70416=a+25\frac{704}{16} = a + 2516704​=a+25 44=a+2544 = a + 2544=a+25

Step 5, Solve for a by subtracting 25 from both sides.

a=44−25=19a = 44 - 25 = 19a=44−25=19 feet

Step 6, Write the final answer. The length of the other parallel side is 191919 feet.

Example 3: Finding the Height of a Trapezium

trapezium

Problem:

Find the altitude of a trapezium whose area is 858585 feet² and the length of the parallel sides are 151515 feet and 252525 feet, respectively.

Step-by-step solution:

Step 1, Identify what we know and what we need to find. We know the area is 858585 feet², and the parallel sides are a = 151515 feet and b = 252525 feet. We need to find the height h.

Step 2, Use the area formula and substitute the known values.

Area=12×(a+b)×h\text{Area} = \frac{1}{2} \times (a + b) \times hArea=21​×(a+b)×h 85=12×(15+25)×h85 = \frac{1}{2} \times (15 + 25) \times h85=21​×(15+25)×h

Step 3, Calculate the sum of the parallel sides.

15+25=4015 + 25 = 4015+25=40 feet

Step 4, Substitute this value into the formula.

85=12×40×h85 = \frac{1}{2} \times 40 \times h85=21​×40×h 85=20×h85 = 20 \times h85=20×h

Step 5, Solve for h by dividing both sides by 202020.

h=8520h = \frac{85}{20}h=2085​ Comments(8)MGMs. GarciaNovember 6, 2025I've used this area of trapezium def for my students. The formula & examples made it easy for them to grasp. Great resource!

WWebDeveloperXenaNovember 4, 2025This glossary page on the area of trapezium is great! I've used it to help my students understand the concept easily. Thanks!

CCanoerCindyNovember 4, 2025I've been struggling to explain trapezium area to my students. This clear def and examples made it click! Thanks for the great resource.

NNatureLover85September 17, 2025I used this page to help my kids with their homework, and the formula explanation was super clear! The examples really helped them understand how to calculate the area of a trapezium step by step. Great resource!

MCMs. CarterSeptember 10, 2025I used this page to explain the area of a trapezium to my 6th grader, and it made a huge difference! The formula was clear, and the examples really helped us practice together. Thanks for making math easier to teach!

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