Calculate Triangle Area: Right Triangle with Base 8 and Height 6

Q: How do I identify the base and height in a right triangle?

In a right triangle, the base and height are the two perpendicular sides that form the 90° angle. The slanted side (hypotenuse) is never used in the area formula!

Q: Why don't we use the hypotenuse (10) in the area formula?

The area formula requires perpendicular measurements. The hypotenuse is diagonal and doesn't give the true height. Only the vertical and horizontal sides work for area calculations.

Q: Can I use any two sides as base and height?

No! You must use the two sides that form the right angle (90°). Using any other combination will give you the wrong area.

Triangle Area Formula with Given Dimensions

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

❤️ 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

00:00 Calculate the triangle's area

00:02 Apply the formula for calculating the triangle area

00:04 (base x height) divided by 2

00:07 Substitute in the relevant values according to the given data and solve to find the area

00:10 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

Step-by-step solution

To find the area of the given triangle, we will follow these steps:

Step 1: Identify the given base and height from the problem.
Step 2: Apply the formula for the area of a triangle.
Step 3: Calculate the area by substituting the values into the formula.

Let's work through the problem:

Step 1: The base $|AB|$ of the triangle is given as 8 units, and the height $|BC|$ is 6 units.

Step 2: The formula for the area of a triangle is:

$A = \frac{1}{2} \times \text{base} \times \text{height}$

Step 3: Substitute the given values into the formula:

$A = \frac{1}{2} \times 8 \times 6$

Perform the multiplication:

$A = \frac{1}{2} \times 48 = 24$

Therefore, the area of the triangle is $\mathbf{24}$ square units.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area = $\frac{1}{2} \times \text{base} \times \text{height}$
Calculation: $\frac{1}{2} \times 8 \times 6 = 24$ square units
Verification: Check that base and height are perpendicular sides ✓

Common Mistakes

Avoid these frequent errors

Using the hypotenuse instead of height
Don't use the hypotenuse (10) as height = Area would be $\frac{1}{2} \times 8 \times 10 = 40$ ! The hypotenuse is the slanted side, not the vertical height. Always use the perpendicular height (6) that forms the right angle.

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 identify the base and height in a right triangle?

In a right triangle, the base and height are the two perpendicular sides that form the 90° angle. The slanted side (hypotenuse) is never used in the area formula!

Why don't we use the hypotenuse (10) in the area formula?

The area formula requires perpendicular measurements. The hypotenuse is diagonal and doesn't give the true height. Only the vertical and horizontal sides work for area calculations.

What if the triangle is rotated differently?

It doesn't matter how the triangle is positioned! Just find the two sides that meet at the right angle - one becomes your base, the other your height.

Can I use any two sides as base and height?

No! You must use the two sides that form the right angle (90°). Using any other combination will give you the wrong area.

How can I check if my answer makes sense?

For a right triangle with sides 6 and 8, the area should be less than the area of a rectangle with the same dimensions (6 × 8 = 48). Since $\frac{1}{2} \times 48 = 24$ , our answer checks out!

🌟 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