Triangle Area Formula: Find Height X When Area = 9 and Base = 3

Q: Why do I need to multiply by 2 when finding height?

The triangle area formula is $ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} $. To solve for height, you need to undo that division by 2 by multiplying both sides by 2!

Q: What if the base is given as the side length instead of the bottom?

Any side of a triangle can be the base! The height is always the perpendicular distance from that base to the opposite vertex. Look for the right angle symbol in the diagram.

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

The height is always marked with a dashed line or shown as perpendicular (90°) to the base. In this problem, the vertical line marked 'x' is the height.

Q: Can I use this formula for any triangle?

Yes! The formula $ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} $ works for all triangles - whether they're right triangles, acute, or obtuse.

Q: What if I get a decimal answer?

Decimal answers are perfectly fine! Just make sure to check your work by substituting back into the original area formula to verify your calculation.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find the height, labeled as X.

00:07 First, we'll use the formula for the area of a triangle.

00:12 It's the base B C times height A E. Then divide by two.

00:17 Now, plug in the given values. Calculate to find height X.

00:26 Multiply everything by two to clear out the fraction.

00:33 Next, let's isolate X.

00:40 And there you have it! That's our solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

The area of the triangle is 9.

Calculate X.

2

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given base and area of the triangle.
Step 2: Apply the triangle area formula to find the height $x$ .
Step 3: Perform the necessary calculations to determine $x$ .

Now, let's work through each step:
Step 1: The problem gives us the base $BC = 3$ and the area of the triangle as $9$ .
Step 2: We'll use the formula $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ .
Step 3: Plugging in our values, the equation becomes $9 = \frac{1}{2} \times 3 \times x$ .
Rearranging for $x$ , we have: $x = \frac{2 \times 9}{3} = \frac{18}{3} = 6$ .

Thus, the solution to the problem is $x = 6$ .

3

Final Answer

6

Key Points to Remember

Essential concepts to master this topic

Area Formula: Use Area = (1/2) × base × height
Technique: Rearrange to height = (2 × Area) ÷ base = 18 ÷ 3
Check: Verify (1/2) × 3 × 6 = 9 square units ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by 2 when solving for height
Don't divide area by base directly = wrong answer! This ignores the 1/2 in the formula and gives height that's half the correct value. Always multiply area by 2 first, then divide by the 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 I need to multiply by 2 when finding height?

+

The triangle area formula is $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ . To solve for height, you need to undo that division by 2 by multiplying both sides by 2!

What if the base is given as the side length instead of the bottom?

+

Any side of a triangle can be the base! The height is always the perpendicular distance from that base to the opposite vertex. Look for the right angle symbol in the diagram.

How do I know which measurement is the height?

+

The height is always marked with a dashed line or shown as perpendicular (90°) to the base. In this problem, the vertical line marked 'x' is the height.

Can I use this formula for any triangle?

+

Yes! The formula $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ works for all triangles - whether they're right triangles, acute, or obtuse.

What if I get a decimal answer?

+

Decimal answers are perfectly fine! Just make sure to check your work by substituting back into the original area formula to verify your calculation.

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Triangle Area Formula: Find Height X When Area = 9 and Base = 3

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