Calculate Triangle Height h: Given Area 70 cm² and Base 14 cm

Q: Why do I multiply by 2 when finding the height?

Because the triangle area formula is $ S = \frac{1}{2} \times b \times h $. To solve for h, you need to undo that division by ½, which means multiplying by 2!

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

The base is the side that the height is perpendicular to. In this problem, FE (14 cm) is the base, and h is the perpendicular distance from vertex D to side FE.

Q: How do I check if my height calculation is correct?

Substitute back into the original formula: $ S = \frac{1}{2} \times 14 \times 10 = 70 $ cm². If you get the given area, your answer is right!

Triangle Area Formula with Height Calculation

The area of triangle DEF is 70 cm².

Calculate h given that the length of side FE is 14 cm.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's find the height of triangle H.

00:12 We'll use the formula for the area of a triangle.

00:15 That's base F E times height H, divided by 2.

00:23 Now, insert the given values into the formula.

00:31 Calculate it, and solve for height H.

00:35 Next, we isolate H on one side.

00:43 And that's our solution! Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The area of triangle DEF is 70 cm².

Calculate h given that the length of side FE is 14 cm.

Step-by-step solution

To determine the height $h$ of triangle DEF given its area is 70 cm² and the side FE is 14 cm, we follow these steps:

Identify the known elements: The base $b$ is 14 cm and the area $S$ is 70 cm².
Use the area formula for a triangle:
$S = \frac{1}{2} \times b \times h$ .
Rearrange the formula to solve for $h$ :
$h = \frac{2 \times S}{b}$ .
Substitute the given values into the formula:
$h = \frac{2 \times 70}{14}$ .
Simplify the calculation:
$h = \frac{140}{14} = 10$ cm.

Therefore, the height $h$ of triangle DEF is $10$ cm.

Final Answer

10 cm

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals half times base times height
Technique: Rearrange to h = 2S/b, so h = 2(70)/14 = 10
Check: Verify: ½ × 14 × 10 = 70 cm² ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by 2 when solving for height
Don't use h = S/b instead of h = 2S/b = wrong answer of 5 cm! The formula is S = ½bh, so you need to multiply by 2 to isolate h. Always rearrange the complete formula correctly.

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 multiply by 2 when finding the height?

Because the triangle area formula is $S = \frac{1}{2} \times b \times h$ . To solve for h, you need to undo that division by ½, which means multiplying by 2!

How do I know which side is the base?

The base is the side that the height is perpendicular to. In this problem, FE (14 cm) is the base, and h is the perpendicular distance from vertex D to side FE.

What if I get a decimal answer for the height?

That's completely normal! Heights don't have to be whole numbers. Just make sure to show your work clearly and round appropriately if needed.

Can I use a different side as the base?

Yes! You can use any side as the base, but then you'd need the perpendicular height to that specific side. The area will always be the same: 70 cm².

How do I check if my height calculation is correct?

Substitute back into the original formula: $S = \frac{1}{2} \times 14 \times 10 = 70$ cm². If you get the given area, your answer is right!

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