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The concept of calculating the area of a trapezoid is an essential skill in the field of geometry. A trapezoid is a quadrilateral with one pair of parallel sides, which can make determining its area somewhat complex. However, by utilizing specific formulas and understanding the properties of this shape, one can easily find the area of a trapezoid. In this guide, we will explore the necessary steps to calculate the area of a trapezoid, providing clear explanations and examples along the way. With a basic understanding of geometry and a few simple calculations, you’ll be able to confidently determine the area of any trapezoid you encounter.
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A trapezoid is a quadrilateral with two parallel base sides of different lengths. The formula for calculating the area of a trapezoid is S = ½(b 1 +b 2 )h, where b 1 and b 2 are the lengths of the two bases, and h is the height. If you know the length of the side of an isosceles trapezoid, you can divide the trapezoid into simple shapes to find the height and calculate the area. Finally, you just need to enter the units to complete the problem.
Steps
Calculate the area with the height and lengths of the two base sides
- For example, if the top base has length (b 1 ) = 8 cm and the bottom bottom (b 2 ) = 13 cm, the sum of the lengths of the two bases is: “b = b 1 + b 2 ” = 8 cm + 13 cm = 21 cm.
- The lengths of the two sides are not the height of the trapezoid. The side and the height have the same length only if that side is perpendicular to the base, which is the case with a square trapezoid.
- In the above example, we have “(b)h” = 21 cm x 7 cm = 147 cm 2 .
- In this example, we have the area of trapezoid S = 147 cm 2 / 2 = 73.5 cm 2 ,.
Find the area of a trapezoid if the side lengths are known
- This method is applicable only to isosceles trapezoid.
- For example, a trapezoid has top bottom (b 1 ) = 6 cm, bottom bottom (b 2 ) = 12 cm, let A be the base side of the triangle, we have A = (b 2 – b 1 )/2 = (12 cm – 6 cm)/2 = 3 cm.
- (3 cm) 2 + B 2 = (5 cm) 2
- Squared values: 9 cm +B 2 = 25 cm
- Subtract from both sides of the equation 9: B 2 = 16 cm
- Calculate the square root of both sides: B = 4 cm
Tip: If the equation doesn’t have a perfect square, reduce the square root to the bare minimum and leave the value in the radical sign. For example: √32 = √(16)(2) = 4√2.
- Rewrite the formula: S = (b 1 +b 2 )h
- Substitute the values into the formula: S = (6 cm +12 cm)(4 cm)
- Simplify the expression: S = (18 cm)(4 cm)
- Multiply the terms together: S = 36 cm 2 .
Advice
- If you know the length of the median (the line segment parallel to the bases and passing through the midpoint of the trapezoid), you can multiply by the height to calculate the area. [9] X Research Source
This article is co-authored by a team of editors and trained researchers who confirm the accuracy and completeness of the article.
The wikiHow Content Management team carefully monitors the work of editors to ensure that every article is up to a high standard of quality.
There are 7 references cited in this article that you can see at the bottom of the page.
This article has been viewed 3,824 times.
A trapezoid is a quadrilateral with two parallel base sides of different lengths. The formula for calculating the area of a trapezoid is S = ½(b 1 +b 2 )h, where b 1 and b 2 are the lengths of the two bases, and h is the height. If you know the length of the side of an isosceles trapezoid, you can divide the trapezoid into simple shapes to find the height and calculate the area. Finally, you just need to enter the units to complete the problem.
In conclusion, calculating the area of a trapezoid is a relatively simple process that requires basic knowledge of the trapezoid’s height and the lengths of its bases. By understanding the formula A = (b1 + b2) * h / 2, where A represents the area, b1 and b2 are the lengths of the bases, and h is the height, one can easily find the area of a trapezoid. Additionally, it is important to remember to use consistent units of measurement throughout the calculation and to double-check the inputs to ensure accurate results. With these steps in mind, anyone can calculate the area of a trapezoid confidently and efficiently.
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