Trapezoid Perimeter Calculation: Area = 35 cm² with Given Side Lengths

Q: How do I know which side is the height?

The height is always perpendicular to the parallel bases. In this trapezoid, AD is vertical and connects the two horizontal parallel sides AB (6 cm) and CD (8 cm).

Q: Why can't I just add all the given measurements?

You need all four sides for perimeter, but only three are given directly. The height AD must be calculated using the area formula first.

Q: What if I get the wrong area when I check?

Double-check your arithmetic! Make sure you used $ \frac{(6+8) \times 5}{2} = \frac{70}{2} = 35 $ correctly. The area should match the given 35 cm².

Q: Is BC really 5.5 cm or do I need to calculate it?

BC = 5.5 cm is given in the diagram. This is the slant side of the trapezoid, which you can read directly from the figure and add to your perimeter calculation.

Q: Can I solve this without using the area formula?

No! The area is the only way to find the missing height AD. Without knowing AD = 5 cm, you cannot calculate the complete perimeter of the trapezoid.

Trapezoid Area with Height Calculation

Look at the trapezoid in the figure.

Its area is equal to 35 cm².

Calculate its perimeter.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the perimeter of the trapezoid

00:03 We'll use the formula for calculating the area of a trapezoid

00:07 (Sum of bases(AB+DC) multiplied by height(H)) divided by 2

00:14 Let's substitute appropriate values according to the given data and solve for the height

00:21 In this case, the height is side AD

00:42 Let's isolate AD

00:47 This is the size of AD, now we can calculate the trapezoid's perimeter

00:53 The perimeter of the trapezoid equals the sum of its sides

01:06 Let's substitute the values of the sides and solve for the perimeter

01:19 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the trapezoid in the figure.

Its area is equal to 35 cm².

Calculate its perimeter.

Step-by-step solution

We begin by inserting any given data into the formula to find the area of a trapezoid:

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

We identify AD as the height of the trapezoid

$35=\frac{(6+8)\times AD}{2}$

$35=\frac{14}{2}AD$

$35=7AD$

We then divide the two sections by 7:

$5=AD$

Finally we calculate the perimeter by adding together all the sides as follows:

$5+6+8+5.5=11+8+5.5=19+5.5=24.5$

Final Answer

$24.5$ cm

Key Points to Remember

Essential concepts to master this topic

Formula: Area = (sum of parallel bases × height) ÷ 2
Technique: 35 = (6+8) × h ÷ 2, so 35 = 7h
Check: Perimeter = 6 + 8 + 5 + 5.5 = 24.5 cm ✓

Common Mistakes

Avoid these frequent errors

Adding the slant side without finding height first
Don't add BC (5.5) to the perimeter before finding AD = wrong total! You need the height to verify the area formula works. Always use the area formula to find the missing height first, then add all four sides.

Practice Quiz

Test your knowledge with interactive questions

Given the following trapezoid:

Calculate the area of the trapezoid ABCD.

FAQ

Everything you need to know about this question

How do I know which side is the height?

The height is always perpendicular to the parallel bases. In this trapezoid, AD is vertical and connects the two horizontal parallel sides AB (6 cm) and CD (8 cm).

Why can't I just add all the given measurements?

You need all four sides for perimeter, but only three are given directly. The height AD must be calculated using the area formula first.

What if I get the wrong area when I check?

Double-check your arithmetic! Make sure you used $\frac{(6+8) \times 5}{2} = \frac{70}{2} = 35$ correctly. The area should match the given 35 cm².

Is BC really 5.5 cm or do I need to calculate it?

BC = 5.5 cm is given in the diagram. This is the slant side of the trapezoid, which you can read directly from the figure and add to your perimeter calculation.

Can I solve this without using the area formula?

No! The area is the only way to find the missing height AD. Without knowing AD = 5 cm, you cannot calculate the complete perimeter of the trapezoid.

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Trapezoid Perimeter Calculation: Area = 35 cm² with Given Side Lengths

Trapezoid Area with Height Calculation

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

How do I know which side is the height?

Why can't I just add all the given measurements?

What if I get the wrong area when I check?

Is BC really 5.5 cm or do I need to calculate it?

Can I solve this without using the area formula?

🌟 Unlock Your Math Potential

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