Perimeter of a Trapezoid: Calculate The Missing Side based on the formula

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

$25=4+7+11+x$

$25=22+x$

$25-22=x$

$3=x$

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

• Step 1: Identify the given information
• Step 2: Apply the perimeter formula
• Step 3: Solve for the missing side

Now, let’s work through each step:

Step 1: The problem gives us a trapezoid with a perimeter of 30 cm and known side lengths of 8 cm, 4 cm, and 12 cm.
We let the missing side be $x$ cm.

Step 2: Use the perimeter formula for a trapezoid:

Step 3: Combine the known side lengths:

Solve for $x$:

Therefore, the length of the missing side is 6 cm.

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

• Step 1: Identify the given perimeter and side lengths.
• Step 2: Use the perimeter formula for a trapezoid.
• Step 3: Solve for the missing side $AD$.

Let's begin:

Step 1: We know that the perimeter $P = 42$ cm. The other sides are $AB = 14$ cm, $BC = 7$ cm, and $CD = 12$ cm.

Step 2: The formula for the perimeter is:

$P = AB + BC + CD + AD$

Substituting in the known values:

$42 = 14 + 7 + 12 + AD$

Step 3: Simplify the equation to find $AD$:

$42 = 33 + AD$

Subtract 33 from both sides:

$AD = 42 - 33$

$AD = 9$

Therefore, the length of side $AD$ is $\textbf{9 cm}$.

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

• Step 1: Understand the properties of an isosceles trapezoid.
• Step 2: Use the given information to set up equations for the perimeter.
• Step 3: Solve the equations to find the missing side length.

Now, let's work through each step:

Step 1: An isosceles trapezoid has two parallel sides and two non-parallel sides that are equal in length. Here, the lengths of the parallel sides are given as $X$ and $3X$. Therefore, the non-parallel sides (legs) must each be $Y$.

Step 2: According to the problem, the perimeter of the trapezoid is $4X + 2Y$. The perimeter can also be expressed as the sum of all sides: $X + 3X + Y + Y$.

So we write the equation:
$X + 3X + Y + Y = 4X + 2Y$

Simplify the equation:
$4X + 2Y = 4X + 2Y$

This indicates that the setup is already balanced. Thus, the lengths of the missing sides (non-parallel sides) are each $Y$.

Therefore, the solution to the problem is $Y$.

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 $x = 6$.

To solve for the missing base of the trapezoid, follow these steps:

• Identify given values: Perimeter $P = 34 \, \text{cm}$, base 1 $a = 14 \, \text{cm}$, leg 1 $c = 10 \, \text{cm}$, leg 2 $d = 12 \, \text{cm}$.
• Set up the equation for the perimeter: $P = a + b + c + d = 34$ Substitute known values: $14 + b + 10 + 12 = 34$
• Simplify the equation: $36 + b = 34$
• Solve for $b$: $b = 34 - 36 = -2$

Since a side length cannot be negative, this trapezoid is impossible with these dimensions.

The correct choice is This trapeze is not possible.

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

• Step 1: Calculate the total perimeter as 300% of the known base $17$.
• Step 2: Use the perimeter formula to isolate the unknown base.
• Step 3: Solve for the unknown base.

Now, let's work through each step:
Step 1: Given that the base $17$ is part of the perimeter calculation and that the perimeter is 300% of this base, we have: $P = 3 \times 17 = 51$

Step 2: Using the perimeter formula for a trapezoid $P = a + b + c + d$, where $a = 17$, $c = 8$, $d = 12$, and $b$ is the unknown base, we have: $51 = 17 + 8 + 12 + b$

Step 3: Solve for the unknown base $b$: $51 = 37 + b$ $b = 51 - 37$ $b = 14$

Therefore, the length of the second base of the trapezoid is $14$.