How Do You Find The Perimeter Of A Trapezoid

Download Article

Download Article

A trapezoid is divers equally a quadrilateral with two parallel sides. As with any polygon, to find the perimeter of a trapezoid you lot need to add all four of its sides together. However, oft you will be missing side lengths just take other information, such as the height of the trapezoid, or the angle measurements. Using this information, you lot can utilize rules of geometry and trigonometry to find the unknown lengths of sides.

1. 1

   Set up the formula for perimeter of a trapezoid. The formula is ${\displaystyle P=T+B+L+R}$ , where ${\displaystyle P}$ equals the perimeter of the trapezoid, and the variables ${\displaystyle T}$ equals the length of the top base of the trapezoid, ${\displaystyle B}$ equals the length of the bottom base, ${\displaystyle Fifty}$ equals the length of the left side, and ${\displaystyle R}$ equals the length of the right side.^[1]

2. 2

   Plug the side lengths into the formula. If you do not know the length of all four sides of the trapezoid, you lot cannot use this formula.

   • For example, if you accept a trapezoid with a top base of operations of two cm, a bottom base of operations of 3 cm, and 2 side lengths of one cm, your formula volition await similar this:
     ${\displaystyle P=2+iii+one+one}$

   Advertisement

3. 3

   Add the side lengths together. This volition give you the perimeter of your trapezoid.

Advertisement

1. ane

   Divide the trapezoid into a rectangle and ii right triangles. To do this, describe the height from both meridian vertices.

   • If yous cannot grade two correct triangles considering 1 side of the trapezoid is perpendicular to the base, just note that this side will have the same measurement as the summit, and divide the trapezoid into i rectangle and one correct triangle.

2. 2

   Label each pinnacle line. Since these are opposite sides of a rectangle, they will exist the same length.^[2]

   • For example, if you accept a trapezoid with a superlative of half dozen cm, you should describe a line from each superlative vertex extending downward to the lesser base. Label each line 6 cm.

3. 3

   Label the length of the middle section of the lesser base of operations. (This is the bottom side of the rectangle.) The length will equal the length of the top base (the meridian side of the rectangle), because opposite sides of a rectangle are of equal length.^[iii] If you do not know the length of the elevation base, you cannot utilize this method.

   • For example, if the top base of the trapezoid is 6 cm, and so the center section of the bottom base of operations is likewise 6 cm.

4. iv

   Set the Pythagorean Theorem formula for the beginning right triangle. The formula is ${\displaystyle a^{2}+b^{2}=c^{2}}$ , where ${\displaystyle c}$ is the length of the hypotenuse of the correct triangle (the side opposite the right bending), ${\displaystyle a}$ is the summit of the right triangle, and ${\displaystyle b}$ is the length of the base of the triangle.^[4]

5. 5

6. half dozen

   Square the known values in the equation. Then, subtract to isolate the ${\displaystyle b}$ variable.

7. 7

   Take the square root to detect the value of $$ b {\displaystyle b} . (For complete instructions on how to simplify square roots, you can read Simplify a Square Root.) The event will give you the value of the missing base of operations of your first correct triangle. Label this length on the base of your triangle.

8. 8

   Find the missing length of the second right triangle. To exercise this, fix up the Pythagorean Theorem formula for the 2d triangle, and follow the steps to find the length of the missing side. If you are working with an isosceles trapezoid, which is a trapezoid in which the two non-parallel sides are the same length,^[5] the two right triangles are coinciding, and so you tin can only carry the value from the beginning triangle over to the second triangle.

9. 9

   Add together up all the side lengths of the trapezoid. The perimeter of whatever polygon is the sum of all sides: ${\displaystyle P=T+B+L+R}$ . For the bottom base, you will add together the bottom side of the rectangle, plus the bases of the 2 triangles. You volition probable take square roots in your answer. For complete instructions on how to add foursquare roots, you can read the commodity Add together Square Roots. Y'all can likewise utilise a reckoner to convert the square roots to decimals.

Advertizement

1. 1

   Divide the trapezoid into a rectangle and ii right triangles. To practice this, draw the height from both acme vertices.

   • If you cannot grade two right triangles because one side of the trapezoid is perpendicular to the base of operations, just note that this side will accept the same measurement equally the height, and divide the trapezoid into one rectangle and one right triangle.

2. 2

   Characterization each height line. Since these are opposite sides of a rectangle, they volition exist the aforementioned length.^[6]

   • For example, if you take a trapezoid with a superlative of 6 cm, you should draw a line from each top vertex extending downwardly to the bottom base of operations. Label each line 6 cm.

3. three

   Characterization the length of the center section of the bottom base. (This is the lesser side of the rectangle.) This length volition exist equal to the length of the superlative base, because opposite sides of a rectangle are of equal length.^[vii]

   • For example, if the height base of the trapezoid is half-dozen cm, then the middle department of the lesser base is also 6 cm.

4. 4

5. 5

   Plug the known values into the sine ratio. Brand sure you use the elevation of the triangle as the length of the opposite side in the formula. You will solve for H.

   • For instance, if the given interior angle is 35 degrees, and the height of the triangle is 6 cm, your formula will look like this:
     ${\displaystyle \sin(35)={\frac {6}{H}}}$

6. six

   Observe the sine of the angle. Do this by using the SIN button on a scientific calculator. Plug this value into the ratio.

   • For instance, by using a calculator yous will find that the sine of a 35 degree angle is .5738 (rounded). So your formula will now be:
     ${\displaystyle .5738={\frac {half dozen}{H}}}$

7. 7

   Solve for H. To do this, multiply each side past H, then dissever each side past the angle sine. Or, you can simply divide the summit of the triangle by the angle sine.

8. 8

   Detect the length of the hypotenuse of the second right triangle. Gear up upward the sine ratio ( ${\displaystyle \sin \theta ={\frac {\text{opposite}}{\text{hypotenuse}}}}$ ) for the 2nd given interior angle. This will give you lot the length of the hypotenuse, which is also the first side of the trapezoid.

9. 9

   Set up the Pythagorean Theorem formula for the first right triangle. The Pythagorean Theorem formula is ${\displaystyle a^{two}+b^{2}=c^{2}}$ , where the length of the hypotenuse is ${\displaystyle c}$ , and the height of the triangle is ${\displaystyle a}$ .

10. 10

11. 11

    Solve for $$ b {\displaystyle b} . This will give you the length of base of the first correct triangle, and the first missing section of the trapezoid'south bottom base.

12. 12

13. 13

    Add up all the side lengths of the trapezoid. The perimeter of any polygon is the sum of all sides: ${\displaystyle P=T+B+L+R}$ . For the bottom base, you lot will add the lesser side of the rectangle, plus the bases of the two triangles.

    • For example, ${\displaystyle 6+(eight.5639+vi+6)+x.4566+8.4854=45.5059}$
      So, the guess perimeter of your trapezoid is 45.5059 cm.

Advertisement

Add New Question

• Question

  How tin can I solve the hypotenuse of a right triangle with a elevation of 2ft?

  

  You don't have enough data to find the hypotenuse. You lot would need the lengths of both legs or the size of at least i of the acute angles or the expanse of the triangle.

• Question

  How practise I find the area without knowing the length of the sides of the trapezoid?

  

  You would have to know the summit of the trapezoid (h) and the lengths of both parallel sides (a and b). The surface area formula is [h(a + b)] / two.

• Question

  Why are there so many formulas?

  

  Information technology's because there are several possible sets of known dimensions regarding a trapezoid.

Ask a Question

200 characters left

Include your email address to get a message when this question is answered.

Submit

Advert

• Use the laws of special triangles to find the missing lengths of special triangles without using sine or the Pythagorean Theorem. The laws utilise to a 30-threescore-xc triangle, or a 90-45-45 triangle.

• Utilise a scientific calculator to notice the sine of an bending by entering the bending measurement, then hitting the "SIN" button. You can also use a trigonometry table.

Thanks for submitting a tip for review!

Advertisement

Things Y'all'll Need

• Reckoner
• Pencil
• Paper

About This Article

Article Summary X

To find the perimeter of a trapezoid if you know the length of both sides and the bases, add together the length of all iv sides. If you know the height, both side lengths, and the top base length, depict a straight line down from each summit corner to form a foursquare and 2 triangles. And then, use the Pythagorean Theorem to detect the length of the base of operations of each triangle. Add the length of each triangle base to the length of the superlative base, and so add that to the top base of operations and both sides to go the perimeter. To larn more about using the Pythagorean Theorem, proceed reading!

Did this summary help you lot?

Thank you to all authors for creating a page that has been read 253,376 times.

Did this article help you?

Source: https://www.wikihow.com/Find-the-Perimeter-of-a-Trapezoid

Posted by: richiesalmor1959.blogspot.com

Share this post