Triangle Area 18: Calculate Height X Using Base Length 6

Q: How do I know which measurement is the base and which is the height?

The height is always the perpendicular distance from the vertex to the base. In this triangle, the vertical line marked 'x' is perpendicular to the horizontal base of 6, making x the height.

Q: Why do we multiply by ½ in the area formula?

A triangle is exactly half of a rectangle with the same base and height. So we use $ \frac{1}{2} \times \text{base} \times \text{height} $ to find the triangle's area.

Q: Can I use a different side as the base?

Yes! You can use any side as the base, but then you must use the perpendicular distance to that side as the height. The area will always be the same regardless of which base-height pair you choose.

Q: What if the area formula gives me a negative answer?

Heights and areas are always positive in geometry. If you get a negative result, check your setup - you might have made an error in the equation or arithmetic.

Triangle Area Formula with Height Variable

The area of the triangle is equal to 18.

Calculate X.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine the height X

00:03 Apply the formula for calculating the area of a triangle

00:06 (base(BC) x height(AE)) divided by 2

00:12 Substitute in the relevant values and proceed to calculate to determine the height X

00:21 Divide 6 by 2 to obtain 3

00:28 Isolate X

00:35 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The area of the triangle is equal to 18.

Calculate X.

Step-by-step solution

To solve for $x$ , we begin by applying the formula for the area of a triangle:

\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}

Given: the area is 18, AE is the height (6) , and EC is the x.

Insert the known values into the formula:

18 = \frac{1}{2} \times 6 \times x

Simplify the equation:

18 = 3x

Next, solve for $x$ by dividing both sides by 3:

x = \frac{18}{3}

Calculate:

x = 6

Thus, the length $x$ is $\mathbf{6}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Area Formula: Triangle area equals one-half times base times height
Technique: Substitute known values: 18 = ½ × 6 × x = 3x
Check: Verify answer by substituting back: ½ × 6 × 6 = 18 ✓

Common Mistakes

Avoid these frequent errors

Confusing base and height measurements
Don't assume the horizontal line is always the base = wrong calculation! The base could be any side, and the height must be perpendicular to that base. Always identify which measurement represents the base and which represents the perpendicular height.

Practice Quiz

Test your knowledge with interactive questions

Angle A is equal to 30°.
Angle B is equal to 60°.
Angle C is equal to 90°.

Can these angles form a triangle?

FAQ

Everything you need to know about this question

How do I know which measurement is the base and which is the height?

The height is always the perpendicular distance from the vertex to the base. In this triangle, the vertical line marked 'x' is perpendicular to the horizontal base of 6, making x the height.

Why do we multiply by ½ in the area formula?

A triangle is exactly half of a rectangle with the same base and height. So we use $\frac{1}{2} \times \text{base} \times \text{height}$ to find the triangle's area.

What if I get a decimal or fraction for the height?

That's completely normal! Triangle heights can be any positive number. Just make sure your calculation is correct by substituting back into the area formula.

Can I use a different side as the base?

Yes! You can use any side as the base, but then you must use the perpendicular distance to that side as the height. The area will always be the same regardless of which base-height pair you choose.

What if the area formula gives me a negative answer?

Heights and areas are always positive in geometry. If you get a negative result, check your setup - you might have made an error in the equation or arithmetic.

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