Calculate Rectangle Perimeter: Finding Total Length with AB=5, CD=7

Q: How do I know which sides to add?

Add all four sides shown in the diagram: AB, CD, AC, and BD. The perimeter is always the total distance around the outside of any shape.

Q: What if I accidentally used the rectangle formula?

If you used $ 2(l+w) $, you'd get $ 2(5+7) = 24 $, which is incorrect. Always check the diagram to see if opposite sides are actually equal before using rectangle shortcuts.

Q: Can I double-check my addition?

Yes! Break it down: $ 5 + 7 = 12 $, then $ 4 + 4 = 8 $, finally $ 12 + 8 = 20 $. Or add in order: $ 5 + 7 + 4 + 4 = 20 $.

Q: Why do AC and BD both equal 4?

In this particular quadrilateral, the diagonals AC and BD happen to have the same length (4 units each). This is just a coincidence - it doesn't make this shape a rectangle.

Perimeter Calculation with Mixed Side Lengths

AB = 5

CD = 7

AC = 4

BD = 4

Calculate the perimeter of the rectangle.

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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

00:03 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

00:25 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 = 5

CD = 7

AC = 4

BD = 4

Calculate the perimeter of the rectangle.

Step-by-step solution

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 $20$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Perimeter equals the sum of all four sides
Technique: Add each side: $5 + 7 + 4 + 4 = 20$
Check: Verify all sides are included and arithmetic is correct ✓

Common Mistakes

Avoid these frequent errors

Confusing this with a rectangle and using 2(l+w)
Don't assume this is a rectangle and use $2(5+7) = 24$ ! The diagram shows a quadrilateral with four different side measurements, not opposite sides being equal. Always add all four given sides: $5 + 7 + 4 + 4 = 20$ .

Practice Quiz

Test your knowledge with interactive questions

Given the trapezoid:

What is the area?

FAQ

Everything you need to know about this question

Why isn't this calculated like a rectangle perimeter?

Even though the problem mentions "rectangle" in the title, the diagram shows a quadrilateral with four different side lengths. A true rectangle would have opposite sides equal, but here we have AB=5, CD=7, AC=4, and BD=4.

How do I know which sides to add?

Add all four sides shown in the diagram: AB, CD, AC, and BD. The perimeter is always the total distance around the outside of any shape.

What if I accidentally used the rectangle formula?

If you used $2(l+w)$ , you'd get $2(5+7) = 24$ , which is incorrect. Always check the diagram to see if opposite sides are actually equal before using rectangle shortcuts.

Can I double-check my addition?

Yes! Break it down: $5 + 7 = 12$ , then $4 + 4 = 8$ , finally $12 + 8 = 20$ . Or add in order: $5 + 7 + 4 + 4 = 20$ .

Why do AC and BD both equal 4?

In this particular quadrilateral, the diagonals AC and BD happen to have the same length (4 units each). This is just a coincidence - it doesn't make this shape a rectangle.

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