How Do You Find the Perimeter of a Trapezoid if You Know Both Base and 1 Height

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A trapezoid is defined as a quadrilateral with ii parallel sides. Equally with any polygon, to find the perimeter of a trapezoid you lot need to add all iv of its sides together. Nevertheless, often you lot will be missing side lengths only have other information, such as the height of the trapezoid, or the angle measurements. Using this information, you tin can apply rules of geometry and trigonometry to observe 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, ${\displaystyle L}$ equals the length of the left side, and ${\displaystyle R}$ equals the length of the right side.^[one]

2. two

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

   • For example, if you have a trapezoid with a top base of 2 cm, a bottom base of three cm, and 2 side lengths of 1 cm, your formula will look like this:
     ${\displaystyle P=2+iii+one+1}$

   Advertizing

3. iii

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

   Advert

1. 1

   Separate the trapezoid into a rectangle and two right triangles. To do this, draw the pinnacle from both summit vertices.

   • If you cannot grade two right triangles considering one side of the trapezoid is perpendicular to the base, just note that this side will take the aforementioned measurement as the height, and split the trapezoid into one rectangle and one right triangle.

2. 2

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

   • For example, if you have a trapezoid with a top of 6 cm, you should describe a line from each top vertex extending down to the bottom base. Label each line half-dozen cm.

3. 3

   Label the length of the middle section of the lesser base of operations. (This is the lesser 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.^[3] If you do not know the length of the top base, yous cannot use this method.

   • For example, if the peak base of the trapezoid is half dozen cm, then the middle section of the bottom base of operations is as well 6 cm.

4. 4

   Set up the Pythagorean Theorem formula for the first right triangle. The formula is ${\displaystyle a^{ii}+b^{2}=c^{2}}$ , where ${\displaystyle c}$ is the length of the hypotenuse of the right triangle (the side opposite the correct angle), ${\displaystyle a}$ is the height of the right triangle, and ${\displaystyle b}$ is the length of the base of operations of the triangle.^[four]

5. five

6. half dozen

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

7. 7

   Accept the square root to observe the value of $$ b {\displaystyle b} . (For complete instructions on how to simplify square roots, you lot tin read Simplify a Square Root.) The result volition give you the value of the missing base of your beginning right triangle. Label this length on the base of your triangle.

8. 8

   Discover the missing length of the second right triangle. To do this, set 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, so you lot can simply carry the value from the first triangle over to the second triangle.

9. 9

   Add upwardly all the side lengths of the trapezoid. The perimeter of any polygon is the sum of all sides: ${\displaystyle P=T+B+50+R}$ . For the bottom base, you will add the bottom side of the rectangle, plus the bases of the two triangles. Yous will probable have foursquare roots in your answer. For complete instructions on how to add together square roots, you tin read the article Add Square Roots. You tin can also utilize a calculator to catechumen the foursquare roots to decimals.

   Advertizing

1. 1

   Dissever the trapezoid into a rectangle and two right triangles. To do this, draw the peak from both top vertices.

   • If you lot cannot form two right triangles because ane side of the trapezoid is perpendicular to the base, only note that this side will have the same measurement every bit the elevation, and split up the trapezoid into one rectangle and 1 correct triangle.

2. 2

   Characterization each superlative line. Since these are opposite sides of a rectangle, they volition be the same length.^[6]

   • For example, if you have a trapezoid with a height of six cm, you should draw a line from each tiptop vertex extending down to the bottom base of operations. Label each line vi cm.

3. 3

   Label the length of the center department of the lesser base. (This is the bottom side of the rectangle.) This length volition be equal to the length of the summit base, considering opposite sides of a rectangle are of equal length.^[vii]

   • For case, if the pinnacle base of the trapezoid is 6 cm, then the center department of the lesser base is too 6 cm.

4. 4

5. 5

   Plug the known values into the sine ratio. Brand certain yous employ the summit of the triangle as the length of the opposite side in the formula. You lot volition solve for H.

   • For case, if the given interior angle is 35 degrees, and the meridian of the triangle is 6 cm, your formula will await similar this:
     ${\displaystyle \sin(35)={\frac {vi}{H}}}$

6. half dozen

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

   • For example, by using a calculator you volition find that the sine of a 35 caste bending is .5738 (rounded). So your formula volition now be:
     ${\displaystyle .5738={\frac {half-dozen}{H}}}$

7. 7

   Solve for H. To do this, multiply each side by H, so divide each side by the angle sine. Or, you lot can simply divide the height of the triangle by the angle sine.

8. 8

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

9. 9

   Fix 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 summit of the triangle is ${\displaystyle a}$ .

10. 10

11. 11

    Solve for $$ b {\displaystyle b} . This volition give y'all the length of base of the first correct triangle, and the start missing section of the trapezoid's bottom base.

12. 12

13. thirteen

    Add together 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 will add the bottom side of the rectangle, plus the bases of the two triangles.

    • For case, ${\displaystyle half-dozen+(eight.5639+6+6)+10.4566+viii.4854=45.5059}$
      So, the approximate perimeter of your trapezoid is 45.5059 cm.

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Add New Question

• Question

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

  

  You lot don't have enough information to find the hypotenuse. You would need the lengths of both legs or the size of at to the lowest degree one of the astute angles or the area of the triangle.

• Question

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

  

  Yous would have to know the height of the trapezoid (h) and the lengths of both parallel sides (a and b). The area formula is [h(a + b)] / 2.

• Question

  Why are there so many formulas?

  

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

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

• Use a scientific calculator to find the sine of an bending by inbound the angle measurement, then hitting the "SIN" button. Y'all can likewise use a trigonometry table.

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Commodity Summary Ten

To find the perimeter of a trapezoid if you know the length of both sides and the bases, add together the length of all 4 sides. If you know the elevation, both side lengths, and the tiptop base length, draw a directly line downwards from each meridian corner to grade a square and 2 triangles. Then, use the Pythagorean Theorem to find the length of the base of each triangle. Add the length of each triangle base of operations to the length of the acme base of operations, so add that to the elevation base and both sides to get the perimeter. To acquire more about using the Pythagorean Theorem, keep reading!

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