Triangle Area Problem: Find Height X When Area = 12 and Base = 3

Q: Why do we multiply the area by 2 when finding height?

Because the area formula is $ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} $. To isolate height, we need to undo the division by 2, which means multiplying by 2!

Q: Can I use any side as the base?

Yes! Any side can be the base, but then you need the perpendicular height to that base. In this problem, the base is clearly marked as 3, and x is the perpendicular height.

Q: How do I know which line segment is the height?

The height is always the perpendicular distance from a vertex to the opposite side (base). Look for the dotted line or right angle symbol - that's your height!

Triangle Area Formula with Height Calculation

The area of the triangle is 12.

Calculate X.

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 First, let's find the height, which we'll call X.

00:09 We use the formula for the area of a triangle.

00:12 That's base times height. Then divide by two.

00:18 Now, plug in the numbers you have and solve for X.

00:29 To isolate X, let's get it alone on one side.

00:47 Divide twelve by three. Almost there!

00:51 And there you have it! That's your solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The area of the triangle is 12.

Calculate X.

Step-by-step solution

To solve this problem, we'll use the formula for the area of a triangle:

Step 1: Identify the given information: Area = 12, base $BC = 3$ , height $AE = x$ .
Step 2: Use the area formula: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ .
Step 3: Solve for $x$ (height) using $x = \frac{2 \times \text{Area}}{\text{base}}$ .

Now, substituting the known values into the equation, we get:

$x = \frac{2 \times 12}{3}$

Performing the multiplication and division yields:

$x = \frac{24}{3} = 8$

Therefore, the length of $x$ is 8.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area = ½ × base × height for any triangle
Technique: Rearrange to height = (2 × Area) ÷ base = (2 × 12) ÷ 3
Check: Substitute back: ½ × 3 × 8 = 12 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply area by 2 when solving for height
Don't use height = Area ÷ base = 12 ÷ 3 = 4! This skips the factor of ½ in the area formula and gives the wrong answer. Always rearrange the complete formula: height = (2 × Area) ÷ base.

Practice Quiz

Test your knowledge with interactive questions

Calculate the area of the triangle using the data in the figure below.

FAQ

Everything you need to know about this question

Why do we multiply the area by 2 when finding height?

Because the area formula is $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ . To isolate height, we need to undo the division by 2, which means multiplying by 2!

Can I use any side as the base?

Yes! Any side can be the base, but then you need the perpendicular height to that base. In this problem, the base is clearly marked as 3, and x is the perpendicular height.

What if I get a decimal answer instead of a whole number?

That's completely normal! Triangle heights can be any positive number. Just make sure your decimal makes sense when you check your work by substituting back into the area formula.

How do I know which line segment is the height?

The height is always the perpendicular distance from a vertex to the opposite side (base). Look for the dotted line or right angle symbol - that's your height!

What happens if I accidentally use the wrong base measurement?

You'll get the wrong height! Always make sure you're using the measurement that corresponds to the base you've chosen. In this problem, the base is clearly labeled as 3.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Triangle questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime