Triangle Area Calculation: Using Height 6 and Base 9

Q: Why do we multiply by 1/2 for triangle area?

A triangle is exactly half of a rectangle with the same base and height. The $ \frac{1}{2} $ accounts for this relationship!

Q: How do I identify the base and height in the diagram?

The base is any side of the triangle (here BC = 9). The height is the perpendicular distance from the opposite vertex to that base (here AD = 6, shown as a dashed line).

Q: Does it matter which side I choose as the base?

No! You can use any side as the base, but then you must use the height that's perpendicular to that specific base. The area will always be the same.

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 - right, acute, or obtuse!

Triangle Area with Base and Height

Look at the triangle below.

BC = 9

AD = 6

Calculate the area of triangle ABC.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the triangle's area

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

00:08 (base x height) ➗ 2

00:21 Substitute in the relevant values according to the given data and proceed to solve to determine the area

00:38 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the triangle below.

BC = 9

AD = 6

Calculate the area of triangle ABC.

Step-by-step solution

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

Step 1: Identify the base and the height of the triangle.
Step 2: Apply the area formula for a triangle.
Step 3: Calculate the area using the given values.

Now, let's apply these steps:

Step 1: From the problem, $BC = 9$ is the base and $AD = 6$ is the height.

Step 2: The area of a triangle is given by the formula $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ .

Step 3: Substitute the given values into the formula:
$\text{Area} = \frac{1}{2} \times 9 \times 6 = \frac{1}{2} \times 54 = 27$ .

Therefore, the area of triangle $\triangle ABC$ is $27$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals one-half times base times height
Technique: Multiply $\frac{1}{2} \times 9 \times 6 = 27$
Check: Verify base is 9, height is 6, calculation gives 27 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by one-half
Don't just multiply base times height = 9 × 6 = 54! This gives the area of a rectangle, not a triangle. Always multiply by $\frac{1}{2}$ to get the triangle area formula.

Practice Quiz

Test your knowledge with interactive questions

Is DE side in one of the triangles?

FAQ

Everything you need to know about this question

Why do we multiply by 1/2 for triangle area?

A triangle is exactly half of a rectangle with the same base and height. The $\frac{1}{2}$ accounts for this relationship!

How do I identify the base and height in the diagram?

The base is any side of the triangle (here BC = 9). The height is the perpendicular distance from the opposite vertex to that base (here AD = 6, shown as a dashed line).

Does it matter which side I choose as the base?

No! You can use any side as the base, but then you must use the height that's perpendicular to that specific base. The area will always be the same.

What if I get a decimal answer?

That's perfectly normal! Many triangles have decimal areas. Just make sure to show your work and round appropriately if needed.

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 - right, acute, or obtuse!

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