How to find Area of a Trapezoid Worksheet, Formula, and Examples

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Key Points about Finding the Area of a Trapezoid

The area of a trapezoid is the amount of space inside the figure, and it is calculated using the formula (base 1 + base 2) / 2 x height.
If the height of a trapezoid is not given, there are other methods that can be used to find the area, such as breaking the trapezoid down into simpler shapes.
Trapezoids come in many different shapes and sizes, and they are used in a variety of fields, from architecture to engineering to physics.

Here’s how to find Area of a Trapezoid

The area of a trapezoid is a fundamental concept in geometry that is used in many different fields, from architecture to engineering to physics. A trapezoid is a four-sided figure that has two parallel sides and two non-parallel sides, which are called the bases. The height of a trapezoid is the perpendicular distance between the two bases.

The formula for finding the area of a trapezoid is (base 1 + base 2) / 2 x height. This formula can be used to calculate the area of any trapezoid, regardless of its size or shape. However, if the height of the trapezoid is not given, it can be difficult to determine the area using this formula. There are other methods that can be used to find the area of a trapezoid without knowing its height, such as breaking the trapezoid down into simpler shapes.

A trapezoid is a 2-D four sided figure that has one set of parallel sides. The other two sides are not parallel. The parallel sides of a trapezoid will be different lengths. In order to solve how to find the Area of a Trapezoid you must add the two parallel sides together, multiply that sum by the height, and then finally divide by two. The height of a trapezoid must be perpendicular to the base of the trapezoid. When finding the Area of a Trapezoid you cannot use the sides of the trapezoid because they are not perpendicular with the base of the trapezoid. Typically, you will see a dotted line in a trapezoid that represents the height.

Common Core Standard: 6.G.1
Related Topics: Area of a Triangle, Area of a Parallelogram, Area of Composite Figures
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How to find Area of a Trapezoid

Definition of Trapezoid

A trapezoid is a quadrilateral with at least one pair of parallel sides. In other words, it is a four-sided polygon with two sides parallel to each other. The parallel sides are called the bases, and the non-parallel sides are called the legs. The height of the trapezoid is the perpendicular distance between the two bases.

Trapezoids can be classified into different types based on the length of their sides and angles. Some common types of trapezoids are isosceles trapezoids, right trapezoids, and scalene trapezoids.

An isosceles trapezoid has two equal sides and two equal angles. The bases of an isosceles trapezoid are parallel, and the legs are congruent. A right trapezoid has one right angle, and the other three angles are acute. The legs of a right trapezoid are perpendicular to the bases. A scalene trapezoid has no equal sides or angles.

Trapezoids are commonly encountered in geometry problems involving area and perimeter. The formula for the area of a trapezoid is (a+b)h/2, where a and b are the lengths of the two bases, and h is the height of the trapezoid. The perimeter of a trapezoid is the sum of the lengths of its four sides.

In summary, a trapezoid is a four-sided polygon with two parallel sides. It can be classified into different types based on the length of its sides and angles. Trapezoids are commonly used in geometry problems involving area and perimeter.

Area of a Trapezoid Formula

The area of a trapezoid is the amount of space inside the trapezoid. It can be calculated using a simple formula that involves the height and the lengths of the two parallel bases.

The formula for the area of a trapezoid is:

A = (a + b) / 2 * h

where a and b are the lengths of the two parallel bases, and h is the height of the trapezoid.

To use this formula, simply add the lengths of the two parallel bases together, and then multiply by the height. Finally, divide the result by 2 to get the area of the trapezoid.

It is important to note that the height of the trapezoid must be perpendicular to the two parallel bases for this formula to work. If the height is not perpendicular, a different formula must be used to calculate the area.

The formula for the area of a trapezoid is very useful in many real-world applications, such as calculating the area of a roof or the amount of material needed to cover a trapezoidal-shaped surface. It is also a fundamental concept in geometry and is often taught in mathematics courses.

In summary, the formula for the area of a trapezoid is (a + b) / 2 * h, where a and b are the lengths of the two parallel bases, and h is the height of the trapezoid. This formula is used to calculate the amount of space inside a trapezoid and is an important concept in geometry and mathematics.

How to Find Area of a Trapezoid without Height

When finding the area of a trapezoid, the height is a crucial factor. However, sometimes the height is not given, and it can be challenging to find it. In such cases, there are alternative methods to find the area of a trapezoid without height.

One such method is to use the length of the two bases and the length of the two diagonals of the trapezoid. The formula to find the area of a trapezoid without height is:

Area = (a + c) / 4(a - c) * √(a + b - c + d)(a - b - c + d)(a + b - c - d)(-a + b + c + d)

Here, a and c are the lengths of the two parallel sides (the bases), and b and d are the lengths of the two diagonals of the trapezoid.

To use this formula, you need to know the values of a, b, c, and d. Once you have these values, you can plug them into the formula and solve for the area.

Another method to find the area of a trapezoid without height is to use the Pythagorean theorem. If you draw a perpendicular line from one of the vertices of the trapezoid to the opposite base, you create a right triangle. You can then use the Pythagorean theorem to find the height of the trapezoid.

To use this method, you need to know the lengths of the two bases and one of the diagonals of the trapezoid. Once you have these values, you can use the Pythagorean theorem to find the height and then use the formula for the area of a trapezoid.

In conclusion, finding the area of a trapezoid without height can be challenging, but there are alternative methods to do so. By using the lengths of the two bases and the two diagonals or the Pythagorean theorem, you can find the area of a trapezoid without knowing the height.

How to find Area of a Trapezoid Solution

4 Simple Steps for Solving Area of a Trapezoid Examples

A trapezoid is a four-sided polygon with two parallel sides, also known as bases. The formula to calculate the area of a trapezoid is (a+b) * h / 2, where a and b are the lengths of the parallel sides and h is the distance between the parallel sides. Here are some examples of how to calculate the area of a trapezoid.

Add the lengths of the two parallel sides together.
Multiply the sum of the two parallel sides times the height.
Divide the answer by two.
Make sure you use the correct unit measure.

Example 1

Suppose there is a trapezoid with a base of 5 cm and 10 cm, and a height of 8 cm. To find the area of the trapezoid, use the formula:

A = (a + b) * h / 2
A = (5 + 10) * 8 / 2
A = 75 cm^2

Therefore, the area of the trapezoid is 75 square centimeters.

Example 2

Consider a trapezoid with a base of 12 cm and 16 cm, and a height of 6 cm. To find the area of the trapezoid, use the formula:

A = (a + b) * h / 2
A = (12 + 16) * 6 / 2
A = 84 cm^2

Hence, the area of the trapezoid is 84 square centimeters.

Example 3

Suppose there is a trapezoid with a base of 3 cm and 7 cm, and a height of 4 cm. To find the area of the trapezoid, use the formula:

A = (a + b) * h / 2
A = (3 + 7) * 4 / 2
A = 20 cm^2

Therefore, the area of the trapezoid is 20 square centimeters.

These examples demonstrate how to calculate the area of a trapezoid using the formula. By knowing the lengths of the parallel sides and the height, one can easily find the area of a trapezoid.

5 Quick Area of a Trapezoid Practice Problems

Area of a Trapezoid Explained

Calculating the area of a trapezoid is a fundamental concept in geometry. The area of a trapezoid is the amount of space inside its boundaries, and it is measured in square units. The formula for calculating the area of a trapezoid is (a + b) * h / 2, where a and b are the lengths of the bases and h is the height of the trapezoid.

Bases and Height

The bases of a trapezoid are the parallel sides of the trapezoid. The height of a trapezoid is the perpendicular distance between the bases. To calculate the area of a trapezoid, you need to know the lengths of the two bases and the height.

Legs and Angles

The legs of a trapezoid are the non-parallel sides of the trapezoid. The median of a trapezoid is the line segment that connects the midpoints of the legs. The midsegment of a trapezoid is the line segment that connects the midpoints of the bases. The midsegment of a trapezoid is parallel to the bases, and its length is equal to the average of the lengths of the bases.

The angles of a trapezoid can be acute, right, or obtuse. An acute trapezoid has all angles less than 90 degrees. A right trapezoid has one right angle. An obtuse trapezoid has one angle greater than 90 degrees. The sum of the angles in a trapezoid is always equal to 360 degrees.

In conclusion, calculating the area of a trapezoid is a simple process once you know the formula. With the knowledge of the bases and height, you can easily calculate the area. The legs and angles of a trapezoid are also important concepts to understand.

Types of Trapezoids

A trapezoid is a quadrilateral with at least one pair of parallel sides. Trapezoids can be classified into different types based on the angles and sides of the shape. In this section, we will discuss the different types of trapezoids.

Isosceles Trapezoid

An isosceles trapezoid is a trapezoid with two parallel sides of equal length. The non-parallel sides are also equal in length. The angles between the parallel sides and non-parallel sides are also equal. The height of an isosceles trapezoid is the perpendicular distance between the parallel sides.

Right Trapezoid

A right trapezoid is a trapezoid with one right angle. The height of a right trapezoid is the length of the perpendicular line segment drawn from the right angle to the base. The length of the two non-parallel sides of a right trapezoid can be calculated using the Pythagorean theorem.

Obtuse Trapezoid

An obtuse trapezoid is a trapezoid with one obtuse angle. The height of an obtuse trapezoid is the length of the perpendicular line segment drawn from the parallel side to the base. The length of the two non-parallel sides of an obtuse trapezoid can be calculated using the Law of Cosines.

In summary, trapezoids can be classified based on their angles and sides. Isosceles trapezoids have two parallel sides of equal length, right trapezoids have one right angle, and obtuse trapezoids have one obtuse angle. The height of a trapezoid is the perpendicular distance between the parallel sides, and can be calculated using different formulas depending on the type of trapezoid.

FAQ about how to Find Area of a Trapezoid

How do I calculate the area of an irregular trapezoid?

To calculate the area of an irregular trapezoid, you need to divide it into simple shapes such as triangles and rectangles. Then, you can calculate the area of each shape and add them together to get the total area of the trapezoid.

What is the formula for finding the perimeter of a trapezoid?

To find the perimeter of a trapezoid, you need to add the lengths of all four sides. The formula for the perimeter of a trapezoid is P = a + b + c + d, where a and b are the lengths of the parallel sides and c and d are the lengths of the non-parallel sides.

What is the formula for finding the area of a right trapezoid?

A right trapezoid is a trapezoid with one right angle. The formula for finding the area of a right trapezoid is A = (a + b) * h / 2, where a and b are the lengths of the parallel sides and h is the height.

How can I find the area of a trapezoid without knowing the height?

If you don’t know the height of a trapezoid, you can use the Pythagorean theorem to calculate it. First, draw an altitude from one of the parallel sides to the other parallel side. This will create two right triangles. Then, you can use the Pythagorean theorem to find the height. Once you know the height, you can use the formula A = (a + b) * h / 2 to find the area.

How do I find the area of a trapezoid with two different heights?

If a trapezoid has two different heights, you can split it into two smaller trapezoids, each with one height. Then, you can use the formula A = (a + b) * h / 2 to find the area of each smaller trapezoid. Finally, you can add the areas of the two smaller trapezoids to get the total area of the original trapezoid.

What is the relationship between the area of a trapezoid and the area of a parallelogram or rhombus?

A trapezoid is a quadrilateral with one pair of parallel sides, while a parallelogram is a quadrilateral with two pairs of parallel sides. The area of a trapezoid is equal to half the sum of the lengths of the parallel sides multiplied by the height. The area of a parallelogram is equal to the base multiplied by the height. Therefore, the area of a trapezoid is half the area of a parallelogram with the same base and height.

A rhombus is a quadrilateral with all sides of equal length. The area of a rhombus is equal to half the product of the lengths of the diagonals. There is no direct relationship between the area of a trapezoid and the area of a rhombus.

Area of a Trapezoid Worksheet Video Explanation

Watch our free video on how to find Area of Trapezoid. This video shows how to solve problems that are on our free Area of Trapezoid worksheet that you can get by submitting your email above.

Watch the free Area of a Trapezoid video on YouTube here: Area of a Trapezoid Video

Video Transcript:

This video is about how to get the area of a trapezoid formula. You can get the trapezoid area worksheet used in this video for free by clicking on the link in the description below. A trapezoid is any four-sided figure that has one set of parallel sides. In order to find area of a trapezoid you’re going to take the length of the longer base, which we’re going to say is b sub 1 plus the length of the shorter base, which is b sub 2 divided by 2 and then multiplying that by the height. This is the general rule for area trapezoid formula.

In the case of this example here, that has a base length of 16, a second base length of 8, and then a height of 12 feet. The bases are the outer edges of the trapezoid. I know that 16 is going to be the longer base because it is the bigger base of the two. 16 is larger than eight so I know it’s the first base. Then we have the second base which is going to be eight feet because it is the shorter length of the two base lengths. And then I know that 12 feet is going to represent the height because it is the distance between the two parallel sides. We know the formula for area of a trapezoid is the long base plus the short base divided by two and then multiplying times the height. In the case of our example we know the long side is 16. We’re going to say 16 plus the short side, which in this case is eight, and then we’re dividing by two and then multiplying by the height which is 12 in this example. When we simplify for our area of a trapezoid, we’re going to do 16 plus 8 which is 24 divided by 2 and then multiplying by 12. Now our area is 24 divided by 2 so that’s 12 and then times 12. We multiply 12 times 12 and that’s going to give us 144. And then our units are feet so it’s 144 feet squared. Our answer to this area of a trapezoid is 144 feet squared. The big thing to remember is that the height is the distance between the two parallel sides and then the bases are the side lengths that are on the outside of the trapezoid area formula.

Let’s do a couple practice problems on our area of a trapezoid worksheet. The first problem on how area of a trapezoid worksheet gives us side lengths of 15 and 4 and a height of 8 inches. In order to show you how to find the area of this trapezoid we’re going to use our formula area equals the long base plus the short base divided by two and then multiplying by the height. In the case of number one I know that the long side is 15 inches and I know that the short side is 4 inches. The height has to be 8 inches because this dotted line represents the distance between the two parallel sides. We take our information and we substitute each piece into our area of a trapezoid formula. The first part is the side length of the long side, which is 15 inches, plus the side length of the short side, which is four inches, and we’re dividing that by 2. And then we multiply all of that with the height, which is 8 inches. Now we’re going to simplify our formula 15 plus 4 is 19 divided by 2 and then times the height which is 8. Then we’re going to simplify 19 divided by 2 and that’s 9.5 and then we’re going to multiply times the height which is 8 to get a solution of 76 inches squared as our final answer.

The second problem showing how to find the area of a trapezoid 6th grade on our area of a trapezoid worksheet that we’re going to use to show you finding the area of a trapezoid is number two. We know our formula is area equals the long side base plus the short side base divided by two and then multiplying times the height. In the case of problem 2 on our area of a trapezoid worksheet we know that the long side is 20 because it’s the outer edge of the trapezoid and it gives us 20. We know the short side is going to be four inches and then we know that the height, which is the distance between the two parallel sides, is going to be 14 inches. Now we’re going to substitute all of them into our formula. The long side is 20 so we’re going to say 20 inches, plus the short side which is 4 inches, so we’re going to say 4 inches, divided by 2 and then multiply times the height, which in this case is 14 inches. Then we’re going to simplify 20 plus 4, that’s 24. We still have to divide by 2 and we still have to multiply times the height which is 14. That final step would be to take the 24 divided by 2 to get 12 and we’re still going to multiply that times the height which is 14 to get a final solution of 168 and our units are inches. The final solution is 168 inches squared.