Calculate Rectangle Perimeter: ABCD with Sides 10.5 and 13

Q: What are AC and BD if they're both 7.5?

AC and BD are the diagonals of the quadrilateral! The fact that they're equal (both 7.5) is actually a property that helps confirm this could be a rectangle, since rectangle diagonals are always equal.

Q: How do I know which measurements are sides vs diagonals?

Look at the vertices! Sides connect adjacent vertices (like A to B), while diagonals connect opposite vertices (like A to C). The diagram shows AC and BD as diagonal lines.

Q: What if this isn't actually a rectangle?

Great observation! Since AB ≠ CD, this is technically a parallelogram, not a rectangle. But the perimeter calculation is the same: add all four sides regardless of the quadrilateral type.

Rectangle Perimeter with Diagonal Measurements

AB = 10.5

CD = 13

AC = 7.5

BD = 7.5

Calculate the perimeter of the rectangle ABCD.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the perimeter of the trapezoid

00:04 The perimeter of the trapezoid equals the sum of its sides

00:11 Let's substitute appropriate values according to the given data and solve for the perimeter

00:28 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

AB = 10.5

CD = 13

AC = 7.5

BD = 7.5

Calculate the perimeter of the rectangle ABCD.

Step-by-step solution

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 $38.5$ .

Final Answer

38.5

Key Points to Remember

Essential concepts to master this topic

Rectangle Property: Opposite sides are equal in length
Technique: Add all four sides: 10.5 + 7.5 + 13 + 7.5
Check: Verify opposite sides match: AB = CD and AC = BD ✓

Common Mistakes

Avoid these frequent errors

Adding only two different sides and doubling
Don't calculate 2(10.5 + 13) = 47! This treats AC and BD as sides when they're actually diagonals. Always identify which measurements are sides versus diagonals before calculating perimeter.

Practice Quiz

Test your knowledge with interactive questions

Given the trapezoid:

What is the area?

FAQ

Everything you need to know about this question

Wait, isn't AB supposed to equal CD in a rectangle?

You're absolutely right to question this! In a true rectangle, opposite sides must be equal. Since AB = 10.5 and CD = 13, this suggests the figure might actually be a parallelogram or the labels are mixed up.

What are AC and BD if they're both 7.5?

AC and BD are the diagonals of the quadrilateral! The fact that they're equal (both 7.5) is actually a property that helps confirm this could be a rectangle, since rectangle diagonals are always equal.

How do I know which measurements are sides vs diagonals?

Look at the vertices! Sides connect adjacent vertices (like A to B), while diagonals connect opposite vertices (like A to C). The diagram shows AC and BD as diagonal lines.

Should I use the Pythagorean theorem here?

Not for finding perimeter! The Pythagorean theorem helps you find missing side lengths, but here all measurements are given. Just add the four sides together.

What if this isn't actually a rectangle?

Great observation! Since AB ≠ CD, this is technically a parallelogram, not a rectangle. But the perimeter calculation is the same: add all four sides regardless of the quadrilateral type.

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