Perimeter of a Trapezoid - Examples, Exercises and Solutions

To find the perimeter we will add all the sides:

$4+5+9+6=9+9+6=18+6=24$

In order to calculate the perimeter of the trapezoid we must add together the measurements of all of its sides:

7+10+7+12 =

36

And that's the solution!

To solve this problem, we'll follow these steps:

• Step 1: Identify the given side lengths of the trapezoid.
• Step 2: Use the perimeter formula for a trapezoid, which is the sum of the lengths of its sides.
• Step 3: Perform the necessary addition to compute the perimeter.

Now, let's work through each step:
Step 1: The trapezoid has side lengths of $9$, $5$, $12$, and $4$.
Step 2: The formula for the perimeter $P$ of a trapezoid is:
$P = \text{side}_1 + \text{side}_2 + \text{side}_3 + \text{side}_4$
Step 3: Plugging in the values, we compute:
$P = 9 + 5 + 12 + 4$
Step 4: Calculating the sum:
$P = 30$

Therefore, the perimeter of the trapezoid is $30$.

To solve this problem, we'll follow these steps:

• Identify the given side lengths of the trapezoid.
• Apply the formula for the perimeter of a trapezoid.
• Perform the addition of all side lengths to calculate the perimeter.

Let's work through each step:

Step 1: Identify the given side lengths. The trapezoid has:

• Top base: $a = 16$
• Bottom base: $b = 1$
• Non-parallel side: $c = 15$
• Other non-parallel side: $d = 16$

Step 2: We'll use the formula for the perimeter of a trapezoid:

$P = a + b + c + d$

Step 3: Plug in the values and perform the calculation:

$P = 16 + 1 + 15 + 16$

$P = 48$

Therefore, the perimeter of the trapezoid is $48$.

To solve this problem, we'll calculate the perimeter of the trapezoid by summing the lengths of its sides:

• Step 1: Identify the side lengths of the trapezoid:
  Top side $= 10$, Bottom side $= 5$, Left side $= 10$, Right side $= 11$.
• Step 2: Apply the perimeter formula:
  The formula for the perimeter $P$ of a trapezoid is $P = a + b + c + d$.
• Step 3: Perform the calculations:
  Substitute the given lengths into the formula:
  $P = 10 + 5 + 10 + 11 = 36$.

Therefore, the perimeter of the trapezoid is $36$.

First, we calculate the long base from the existing data:

Multiply the short base by 1.5:

$5\times1.5=7.5$

Now we will add up all the sides to find the perimeter:

$2+5+3+7.5=7+3+7.5=10+7.5=17.5$

We replace the data in the formula to find the perimeter:

$25=4+7+11+x$

$25=22+x$

$25-22=x$

$3=x$

Since this is an isosceles trapezoid, and the two legs are equal, we can state that:

$AB=CD=6$

Now let's add all the sides together to find the perimeter

$6+6+10+12=$

$12+22=34$

To calculate the perimeter, we add up all the sides:

$10+x+(6+x)+(x+1)$

Now, given that x equals 3, we substitute in the appropriate places:

$10+3+(6+3)+(3+1)=$

$10+3+9+4=$

$13+13=26$

To solve this problem, we'll apply the straightforward approach of summing up the lengths of all four sides of the trapezoid to determine its perimeter:

• Step 1: Identify the side lengths: the top base is $6$, the bottom base is $14.52$, the left side is $4.1$, and the right side is $9.87$.
• Step 2: Apply the perimeter formula for the trapezoid: $P = a + b + c + d$, where $a = 6$, $b = 14.52$, $c = 4.1$, and $d = 9.87$.
• Step 3: Add the side lengths: $P = 6 + 14.52 + 4.1 + 9.87$.

Now, performing the calculation:

Therefore, the perimeter of the trapezoid is $34.49$.

To solve this problem, we'll use the perimeter formula for a trapezoid, which is straightforward since all side lengths are provided:

• Step 1: Identify the side lengths:
  Top base ($a$): $12.28$ units
  Bottom base ($b$): $17.5$ units
  Left non-parallel side ($c$): $5.1$ units
  Right non-parallel side ($d$): $6$ units
• Step 2: Apply the formula for the perimeter, which states:
  $P = a + b + c + d$
• Step 3: Substitute the known values into the formula:
  $P = 12.28 + 17.5 + 5.1 + 6$
• Step 4: Perform the addition:

Calculating the sum:

$12.28 + 17.5 = 29.78$

$29.78 + 5.1 = 34.88$

$34.88 + 6 = 40.88$

Hence, the perimeter of the trapezoid is $40.88$ units.

To solve this problem, we'll utilize the formula for the perimeter of a trapezoid.

The formula for the perimeter is given by:

• $P = a + b + c + d$

From the problem, we know:

• The perimeter $P$ is 36.
• The side lengths are 13, 12, and 5, with the unknown side as $x$.

Plug these into the formula:

$36 = 13 + 12 + 5 + x$

Combine the known side lengths:

$36 = 30 + x$

To isolate $x$, subtract 30 from both sides:

$x = 36 - 30$

Calculate the result:

$x = 6$

Therefore, the length of the missing side $x$ is 6.

Thus, the correct answer is choice 2, corresponding to $x = 6$.

Since ABCD is a trapezoid, one can determine that:

$AD=BC=7$

Thus the formula to find the area will be

$$$S_{ABCD}=\frac{(AB+DC)\times h}{2}$

Since we are given the perimeter of the trapezoid, we can find$AB+DC$

$P_{ABCD}=7+AB+7+DC$

$34=14+AB+DC$

$34-14=AB+DC$

$20=AB+DC$

Now we will place the data we obtained into the formula in order to calculate the area of the trapezoid:

$S=\frac{20\times5}{2}=\frac{100}{2}=50$

We can find the height BE by calculating the trapezoidal area formula:

$S=\frac{(AB+CD)}{2}\times h$

We replace the known data: $9=\frac{(3+6)}{2}\times BE$

We multiply by 2 to get rid of the fraction:

$9\times2=9\times BE$

$18=9BE$

We divide the two sections by 9:

$\frac{18}{9}=\frac{9BE}{9}$

$2=BE$

If we draw the height from A to CD we get a rectangle and two congruent triangles. That is:

$AF=BE=2$

$AB=FE=3$

$ED=CF=1.5$

Now we can find one of the legs through the Pythagorean theorem.

We focus on triangle BED:

$BE^2+ED^2=BD^2$

We replace the known data:

$2^2+1.5^2=BD^2$

$4+2.25=DB^2$

$6.25=DB^2$

We extract the root:

$\sqrt{6.25}=DB$

$2.5=DB$

Now that we have found DB, it can be argued that:

$AC=BD=2.5$

We calculate the perimeter of the trapezoid:$6+3+2.5+2.5=$

$9+5=14$

To find the perimeter of the trapezoid, all its sides must be added:

We will focus on finding the bases.

To find GF we use the Pythagorean theorem: $A^2+B^2=C^2$in the triangle AFG

We replace

$3^2+GF^2=5^2$

We isolate GF and solve:

$9+GF^2=25$

$GF^2=25-9=16$

$GF=4$

We perform the same process with the side DB of the triangle ABD:

$8^2+DB^2=17^2$

$64+DB^2=289$

$DB^2=289-64=225$

$DB=15$

We start by finding FB:

$FB=AB-AF=17-5=12$

Now we reveal EF and CB:

$GF=GE=4$

$DB=DC=15$

This is because in an isosceles triangle, the height divides the base into two equal parts so:

$EF=GF\times2=4\times2=8$

$CB=DB\times2=15\times2=30$

All that's left is to calculate:

$30+8+12\times2=30+8+24=62$