How to Find the Perimeter of a Trapezoid?

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The perimeter of a Trapezoid is similar to that of the rectangle. The Trapezoid is a shape that is diagrammatically given as;

The Perimeter of a Trapezoid Formula

The Perimeter of a Trapezoid is the sum of all the side lengths of the shape. The mathematical formula is denoted as;

P = T + S + B + S

Where;

T = Top of the shape

S = side of the shape

B = Base of the shape

In cases where any side lengths may be missing, the Right Angle-Pythagoras theorem becomes relevant. This formula also employs the same method as the one above. However, you will need to solve for the right angle(s) before they can be used.

An example will be used to explain better.

How to Calculate the Perimeter of the Trapezoid?

As already outlined, two major formulas can be used to calculate the Trapezoid, and their steps will be outlined now.

The Basic Formula Steps

Step 1: Ensure that all of the side lengths ae available

Step 2: Add all the side lengths together to find the perimeter

The Right Angle-Pythagoras Steps

Step 1: you have to confirm that only one of the side lengths is missing and the height is available.

Step 2a: Divide the Trapezoid into a Rectangle and two right angles with the rectangle in the middle of the two.

Step 2b: If the Trapezoid cannot be divided into two right angles and a rectangle due to one side being perpendicular to the bottom base, then Divide into one rectangle and one right angle.

Step 3: Identify the height, length and base of each right angle.

Step 4: use the Pythagoras theorem to find the right angle bases, heights or lengths of each sequential pattern.

Step 5: Find the missing length and add it up to get the perimeter

Calculating the Perimeter of the Trapezoid Using Examples

Example 1

Find the perimeter of the trapezoid

Solution

P = T + S + B + S

Where;

T = 5 cm

S = 7 cm

B = 6 cm

As such;

P = 5 cm + 5 cm + 6 cm + 7 cm

P = 23 cm

Example 2

Calculate the perimeter of the trapezoid below.

Solution

Considering the above example, it is clear that the base length is missing and using the first formula would not be possible now. However, the height from top to bottom was given as 8 cm. As such, the Right Angle-Pythagoras formula will be the best solution to use. With this realization, the first step of the above formula has been satisfied.

Step 2a: Divide the Trapezoid into a Rectangle and two right angles with the rectangle in the middle of the two.

Separating the angles from the rectangle, the formed shape will be

Step 3: Identify the height, length and base of each right angle.

Now we have successfully dissected the Trapezoid such that it becomes two right angles and one rectangle. There are some important points to note in this dissection

Point 1: The top base of the initial Trapezoid was 10 cm and is still so even after the dissection. This is because the top was not in any way affected.

Point 2: the length of the right angles was 8 cm. This is understandable because the initial trapezoid height of 8 cm is what the length of the right angles also share.

Point 3: The right angles hypotenuse is 12 cm each. This is because the hypotenuses are actually the sides of the initial Trapezoid.

Point 4: It is important to recall that it is the bottom base of the Initial Trapezoid that we are to find. Now that bottom base has been shared into three bases (two right angles and one rectangle. Apparently, one of the bases has been found, which is one of the rectangles.

The rectangle was created on the common logic that the top of a rectangle measurement is equal to its bottom.

Point 5: The next step will be to find the right angles bases and add them to the rectangle base. The addition will be the base of the Trapezoid.

Step 4: Use the Pythagoras theorem to find the right angle bases, heights or lengths of each sequential pattern

Since the two right angles have the same hypotenuses and length, we will only need to find one of the bases to get the two.

Using the Pythagoras theorem, it will be

L2 + B2 = H2

82 + B2 = 122  

B2 = 122 – 82

B2 = 144 – 64

B2 = 80

B = 8.944

Since one of the right angles bases is 8.944

Then the two right-angle bases will be 2 x 8.944 = 17.88

Step 5: Find the missing length and add up to get the perimeter

Since the base of the initial Trapezoid = the base of the rectangle and the two triangles, then

B in the trapezoid formula = 10 cm + 17.88 cm

B = 27.88 cm.

Since we have found the base of the Trapezoid, we can now find the perimeter

The perimeter of the Trapezoid will be;

P = T + S + B + S

P = 10 cm + 12 cm + 27.88 cm + 12 cm

P = 61.88 cm

Conclusion

Calculating the Trapezoid Perimeter is straight to the point, as has been seen in this article. While it has a shape similar to the right angle, they are not thesame, and this can be seen in the computation done in this piece. Two examples were considered to show how the perimeter of the shape given certain circumstances. Students can use the two steps to consistently and accurately solve other similar problems.

How to Find the Perimeter of a Trapezoid?

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