Triangle Perimeter Practice Problems & Solutions

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

• Step 1: Gather the given side lengths of quadrilateral ABCD.

• Step 2: Since it's necessary to understand summation, add all lengths.

• Step 3: Conclude from sum.

Now, let's work through each step:

Step 1: The problem provides:
$\begin{aligned} AB &= 10.5, \\ CD &= 13, \\ AC &= 7.5, \\ BD &= 7.5. \end{aligned}$

Step 2: Add them together:
$\begin{aligned} \text{Perimeter} &= AB + CD + AC + BD \\ &= 10.5 + 13 + 7.5 + 7.5. \end{aligned}$

Step 3: Calculate: $\begin{aligned} \text{Perimeter} &= 10.5 + 13 + 7.5 + 7.5 = 38.5. \end{aligned}$

Therefore, the solution is that the perimeter of quadrilateral ABCD is $38.5$ .

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

• Step 1: Identify the given measurements for the sides.

• Step 2: Use the perimeter formula for a trapezoid, which is summing all sides.

• Step 3: Add the values to get the perimeter.

Now, let's work through each step:

Step 1: The problem gives us four sides to consider. These sides are: $AB = 5$, $CD = 7$, $AC = 4$, and $BD = 4$.

Step 2: The perimeter of a trapezoid or any quadrilateral is simply the sum of all four sides. Hence, we need to add $AB$, $CD$, $AC$, and $BD$.

Step 3: Adding the values, we calculate the perimeter:$AB + CD + AC + BD = 5 + 7 + 4 + 4 = 20$.

Therefore, the perimeter of the given shape is $20$.

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

• Step 1: Identify the formula for the circumference of a circle as $C = 2\pi r$.
• Step 2: Substitute the known value of the radius into the formula.
• Step 3: Simplify to find the circumference.

Now, let's work through each step:
Step 1: The formula for the circumference, $C$, is $C = 2\pi r$.
Step 2: Substitute the given radius $r = 3$ cm into the formula:
$C = 2\pi \times 3$.
Step 3: Perform the multiplication:
$C = 6\pi$.
Thus, the circumference of the circle is $6\pi$ cm.

Therefore, the solution to the problem is $6\pi$ cm.

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

• Step 1: Identify the given information
• Step 2: Apply the appropriate perimeter formula for the parallelogram
• Step 3: Perform the necessary calculations

Now, let's work through each step:
Step 1: The problem gives us the lengths of two adjacent sides of the parallelogram: $a = 10$ and $b = 8$.
Step 2: We'll use the formula for the perimeter of a parallelogram: $P = 2(a + b)$.
Step 3: Plugging in our values, we get:

$P = 2(10 + 8) = 2 \times 18 = 36$

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

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

• Step 1: Identify the base and side of the parallelogram from the diagram.
• Step 2: Use the perimeter formula for a parallelogram.
• Step 3: Substitute the values into the formula to find the perimeter.

Now, let's work through each step:
Step 1: From the diagram, the base of the parallelogram is given as $3$ units (top side). Despite the lack of explicit vertical length values, the common approach is to assume symmetrical side lengths—both the base and the side given symmetrically leads us to a second side, typically directly inferred. However, since all clear interpretation points to utilizing 1 and horizontal 3, we verify with associated edge matching.
Step 2: Use the formula for the perimeter of the parallelogram: $P = 2 \times (\text{base} + \text{side})$.
Step 3: Substitute the given values into the formula: $P = 2 \times (3 + 1)$.
Calculating this gives us: $P = 2 \times 4 = 8$.

Therefore, the solution to the problem is $P = 8$.