Calculate Isosceles Trapezoid Perimeter: Finding X When AB=5 and CD=10

Q: What does 'isosceles trapezoid' mean exactly?

An isosceles trapezoid has one pair of parallel sides (bases) and two equal non-parallel sides (legs). This means sides AD and BC are the same length!

Q: How do I know which sides are equal in length?

In trapezoid ABCD, the parallel sides are AB and CD (the bases). The non-parallel sides AD and BC are the legs, and these are equal in an isosceles trapezoid.

Q: Why isn't AC included in the perimeter calculation?

AC is a diagonal of the trapezoid, not a side! Perimeter only includes the four sides that form the boundary: AB, BC, CD, and AD.

Q: Can the perimeter be simplified further than 15 + 2X?

No, this is the simplest form since we don't know the value of X. The perimeter stays as an expression: $15 + 2X$.

Q: What if I mixed up which sides are parallel?

Look at the diagram carefully! The horizontal sides AB (length 5) and CD (length 10) are parallel. The slanted sides AD and BC are the equal legs.

Q: How can I verify my perimeter formula is correct?

Check that you have all four sides: AB = 5, BC = X, CD = 10, AD = X. Add them: 5 + X + 10 + X = 15 + 2X ✓

Isosceles Trapezoid Perimeter with Side Variables

The trapezoid ABCD is isosceles.

AB = 5

CD = 10

AC = X

Calculate the perimeter of the trapezoid.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Express the trapezoid perimeter using X

00:03 It's an isosceles trapezoid, therefore sides are equal

00:14 The trapezoid perimeter equals the sum of its sides

00:23 Let's substitute appropriate values according to the given data and solve for the perimeter

00:34 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

The trapezoid ABCD is isosceles.

AB = 5

CD = 10

AC = X

Calculate the perimeter of the trapezoid.

Step-by-step solution

To determine the perimeter of an isosceles trapezoid ABCD, we must first recognize the properties inherent in the setup.

We are informed that the trapezoid is isosceles, meaning that the non-parallel sides, $AD$ and $BC$ , are equal in length. Thus, by relying on the problem, we recognize that:

The side $AB$ is 5 units long.
The base $CD$ is 10 units long.
The side $AC$ is given as $X$ , which accordingly indicates that $BD = X$ due to the isosceles property.

With $AD = BC = X$ , we can summarize the perimeter formula of the trapezoid as follows:

$P = AB + BC + CD + AD$

This formula simplifies to:

$P = 5 + X + 10 + X$

After combining like terms, we find that the perimeter is:

$P = 15 + 2X$

Thus, the perimeter of the trapezoid ABCD in terms of $X$ is $15 + 2X$ .

Final Answer

$15+2x$

Key Points to Remember

Essential concepts to master this topic

Isosceles Property: Non-parallel sides AD and BC are equal in length
Technique: Identify equal sides: if AC = X, then BD = X
Check: Perimeter formula P = AB + BC + CD + AD = 5 + X + 10 + X ✓

Common Mistakes

Avoid these frequent errors

Confusing diagonal AC with side length
Don't assume AC (diagonal) equals a side length like AD or BC = wrong perimeter calculation! The diagonal connects opposite vertices, not adjacent ones. Always identify that in isosceles trapezoids, the non-parallel sides (legs) are equal: AD = BC = X.

Practice Quiz

Test your knowledge with interactive questions

Given the trapezoid:

What is the area?

FAQ

Everything you need to know about this question

What does 'isosceles trapezoid' mean exactly?

An isosceles trapezoid has one pair of parallel sides (bases) and two equal non-parallel sides (legs). This means sides AD and BC are the same length!

How do I know which sides are equal in length?

In trapezoid ABCD, the parallel sides are AB and CD (the bases). The non-parallel sides AD and BC are the legs, and these are equal in an isosceles trapezoid.

Why isn't AC included in the perimeter calculation?

AC is a diagonal of the trapezoid, not a side! Perimeter only includes the four sides that form the boundary: AB, BC, CD, and AD.

Can the perimeter be simplified further than 15 + 2X?

No, this is the simplest form since we don't know the value of X. The perimeter stays as an expression: $15 + 2X$ .

What if I mixed up which sides are parallel?

Look at the diagram carefully! The horizontal sides AB (length 5) and CD (length 10) are parallel. The slanted sides AD and BC are the equal legs.

How can I verify my perimeter formula is correct?

Check that you have all four sides: AB = 5, BC = X, CD = 10, AD = X. Add them: 5 + X + 10 + X = 15 + 2X ✓

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