Triangle Area Calculation: Express Area Using Height X and Base 6

Triangle Area Formula with Variable Height

Look at the triangle ABC below.

BC = 6

AD = X

Express the area of the triangle using X.

666XXXCCCAAABBBDDD

❤️ 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
00:09 Let's express the area of the triangle using X.
00:13 To do that, apply the formula for a triangle's area.
00:18 So, think of it as base, B.C., times height, H, divided by 2.
00:23 Here, we mark A.D. as our height, H.
00:31 Now, substitute the relevant values into the formula.
00:39 Go ahead and calculate, then solve for X.
00:44 And there you have it, that's your solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the triangle ABC below.

BC = 6

AD = X

Express the area of the triangle using X.

666XXXCCCAAABBBDDD

2

Step-by-step solution

To express the area of triangle △ABC \triangle ABC using X X , follow these steps:

  • Identify the base BC=6 BC = 6 .
  • Identify the height as AD=X AD = X .
  • Use the formula for the area of a triangle: Area=12×base×height \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} .
  • Substitute the known values: Area=12×6×X \text{Area} = \frac{1}{2} \times 6 \times X .
  • Simplify the expression: Area=6X2 \text{Area} = \frac{6X}{2} .
  • Further simplify: Area=3X \text{Area} = 3X .

Comparing this with the choices given, choices B (6X2 \frac{6X}{2} ) and C (3X 3X ) are both valid representations of the area.

Therefore, the correct answer is that choices B and C are correct.

Answers B and C are correct.

3

Final Answer

Answers B and C are correct.

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area equals one-half times base times height
  • Technique: Substitute values: Area=12×6×X=6X2 \text{Area} = \frac{1}{2} \times 6 \times X = \frac{6X}{2}
  • Check: Simplify to verify both forms are equal: 6X2=3X \frac{6X}{2} = 3X ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to divide by 2 in the area formula
    Don't just multiply base × height = 6X! This gives you the area of a rectangle, not a triangle. The triangle area is exactly half the rectangle area. Always use the complete formula: Area = 12×base×height \frac{1}{2} \times \text{base} \times \text{height} .

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 is the area formula divided by 2?

+

A triangle is exactly half of a rectangle! If you draw a rectangle with the same base and height, then draw a diagonal, you get two identical triangles. So the triangle area is half the rectangle area.

Are both 6X2 \frac{6X}{2} and 3X correct answers?

+

Yes! Both expressions represent the same value. 6X2 \frac{6X}{2} shows the calculation step-by-step, while 3X is the simplified form. Both are mathematically equivalent.

How do I identify the height in a triangle?

+

The height is the perpendicular distance from a vertex to the opposite side (base). Look for the line segment that forms a right angle (90°) with the base - that's your height!

What if the height is drawn outside the triangle?

+

That's perfectly normal for obtuse triangles! The height can extend outside the triangle, but the formula Area=12×base×height \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} still works exactly the same way.

Can I use any side as the base?

+

Absolutely! You can choose any side as the base, but then you must use the height that is perpendicular to that specific base. The area will be the same regardless of which base you choose.

🌟 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

More Questions

Click on any question to see the complete solution with step-by-step explanations

Area of a Triangle

Right Triangle Side Length: Finding BC When Area = 10 and Height = 4
Click to solve
Calculate Triangle Height h: Given Area 70 cm² and Base 14 cm
Click to solve