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

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

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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