Calculate Triangle Height DH Using Area 60 cm² and Base 12 units

Q: Why do I need to divide by 2 in the triangle area formula?

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

Q: What if I get the area formula mixed up with other shapes?

Remember: Triangle = 1/2 × base × height, Rectangle = base × height, Circle = $ \pi r^2 $. The triangle always has that crucial 1/2 factor!

Q: Can I solve this problem by rearranging the formula first?

Absolutely! Rearrange $ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} $ to get $ \text{height} = \frac{2 \times \text{Area}}{\text{base}} $, then substitute your values.

Q: Why is the height called DH and not just h?

DH shows the specific line segment from point D perpendicular to base FE, ending at point H. This naming helps identify exactly which measurement we're finding in the diagram.

Triangle Area Formula with Height Calculation

The area of the triangle DEF is 60 cm².

The length of the side FE = 12.

Calculate the height DH.

❤️ 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 height DH

00:03 Observe the sides and lines according to the given data

00:08 Apply the formula for calculating the area of a triangle

00:18 (height x base) divided by 2

00:22 Insert the relevant values and proceed to solve for DH

00:43 Multiply by denominators in order to eliminate the fractions

00:53 Isolate DH

01:18 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The area of the triangle DEF is 60 cm².

The length of the side FE = 12.

Calculate the height DH.

Step-by-step solution

To solve this problem, we'll use the formula for the area of a triangle:

Step 1: Write the formula for the area of a triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ .
Step 2: Substitute the given values: $60 = \frac{1}{2} \times 12 \times \text{DH}$ .
Step 3: Simplify the equation by calculating the half of the base: $\frac{1}{2} \times 12 = 6$ .
Step 4: Replace and solve the equation: $60 = 6 \times \text{DH}$ .
Step 5: Isolate $\text{DH}$ by dividing both sides by 6: $\text{DH} = \frac{60}{6}$ .
Step 6: Calculate the result: $\text{DH} = 10$ .

The height from point D to the base FE, $\text{DH}$ , is 10 cm.

Final Answer

10 cm

Key Points to Remember

Essential concepts to master this topic

Formula: Area = 1/2 × base × height for any triangle
Technique: Substitute known values: 60 = 1/2 × 12 × DH
Check: Verify: 1/2 × 12 × 10 = 60 cm² ✓

Common Mistakes

Avoid these frequent errors

Forgetting to divide by 2 in the area formula
Don't use Area = base × height without the 1/2 = doubles the area calculation! This formula is for rectangles, not triangles. Always use Area = 1/2 × base × height for triangles.

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 divide by 2 in the triangle area formula?

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

How do I identify which side is the base?

Any side can be the base! In this problem, side FE = 12 is given as the base. The height is always perpendicular to the chosen base, which is why DH forms a right angle with FE.

What if I get the area formula mixed up with other shapes?

Remember: Triangle = 1/2 × base × height, Rectangle = base × height, Circle = $\pi r^2$ . The triangle always has that crucial 1/2 factor!

Can I solve this problem by rearranging the formula first?

Absolutely! Rearrange $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ to get $\text{height} = \frac{2 \times \text{Area}}{\text{base}}$ , then substitute your values.

Why is the height called DH and not just h?

DH shows the specific line segment from point D perpendicular to base FE, ending at point H. This naming helps identify exactly which measurement we're finding in the diagram.

🌟 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