Calculate Triangle Area: Using Height 6 and Base 3.5 Units

Q: How do I know which side is the base and which is the height?

The base is any side you choose, and the height is the perpendicular distance from that base to the opposite vertex. In this triangle, the base is 3.5 (horizontal line) and height is 6 (vertical line).

Q: Why do we multiply by 1/2 in the triangle area formula?

A triangle is exactly half of a parallelogram! If you imagine completing the parallelogram, the triangle would be half that area, so we multiply base × height × $ \frac{1}{2} $.

Q: What if I calculated 21 instead of 10.5?

You forgot to multiply by $ \frac{1}{2} $! Remember: always divide by 2 or multiply by 0.5 when finding triangle area. The formula is $ \frac{1}{2} \times \text{base} \times \text{height} $.

Q: Can I use any side as the base?

Yes! You can choose any side as the base, but then you must use the height that is perpendicular to that chosen base. The area will always be the same.

Triangle Area with Given Base and Height

Calculate the area of the triangle below, if possible.

❤️ 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 area of the triangle

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

00:06 (base x height) divided by 2

00:09 Substitute in the relevant values according to the given data and proceed to solve for the area

00:12 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 below, if possible.

Step-by-step solution

To solve this problem, we will determine the area of the triangle using the given base and height. Here are the steps:

Identify the given base and height: base $= 6$ , height $= 3.5$ .
Apply the formula for the area of a triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ .
Substitute the given values into the formula: $\text{Area} = \frac{1}{2} \times 6 \times 3.5$ .
Calculate the area: $= \frac{1}{2} \times 21 = 10.5$ .

Therefore, the area of the triangle is $10.5$ , which matches the correct multiple-choice option provided.

Final Answer

10.5

Key Points to Remember

Essential concepts to master this topic

Formula: Triangle area equals one-half times base times height
Technique: Area = $\frac{1}{2} \times 3.5 \times 6 = 10.5$
Check: Multiply 6 × 3.5 = 21, then divide by 2 ✓

Common Mistakes

Avoid these frequent errors

Confusing base and height measurements
Don't use height as base or vice versa = wrong calculation! In this problem, the base is 3.5 (horizontal) and height is 6 (vertical). Always identify which measurement is perpendicular to 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

How do I know which side is the base and which is the height?

The base is any side you choose, and the height is the perpendicular distance from that base to the opposite vertex. In this triangle, the base is 3.5 (horizontal line) and height is 6 (vertical line).

Why do we multiply by 1/2 in the triangle area formula?

A triangle is exactly half of a parallelogram! If you imagine completing the parallelogram, the triangle would be half that area, so we multiply base × height × $\frac{1}{2}$ .

What if I calculated 21 instead of 10.5?

You forgot to multiply by $\frac{1}{2}$ ! Remember: always divide by 2 or multiply by 0.5 when finding triangle area. The formula is $\frac{1}{2} \times \text{base} \times \text{height}$ .

Can I use any side as the base?

Yes! You can choose any side as the base, but then you must use the height that is perpendicular to that chosen base. The area will always be the same.

How do I check if my answer is reasonable?

Compare your answer to the base and height values. The area (10.5) should be less than base × height (21) since we're finding half of that rectangle!

🌟 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