Triangle Area Calculation: Finding Area with Base 4 and Height 8.5

Q: Why do we divide by 2 in the triangle area formula?

A triangle is exactly half of a rectangle! If you draw a rectangle with the same base and height, the triangle takes up only half that space. That's why we multiply by $ \frac{1}{2} $ or divide by 2.

Q: How do I identify the base and height from the diagram?

The base is any side of the triangle (here it's BC = 4). The height is the perpendicular line from the opposite vertex to that base (here it's AE = 8.5). Look for the right angle symbol!

Q: Can I use a different side as the base?

Absolutely! You can choose any side as the base. Just make sure to use the perpendicular height to that base. Different base-height pairs will give the same area.

Q: How can I check if my triangle area is reasonable?

The area should be less than base × height (the rectangle area)For this problem: 17 The area should be a positive number

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:07 Let's calculate the area of the triangle.

00:10 We'll use the area formula, which is base times height divided by two.

00:15 Here, it's base B C times height A E, all divided by two.

00:21 Plug in the given numbers, and then solve it step by step.

00:32 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Calculate the area of the following triangle:

2

Step-by-step solution

To solve this problem, we'll use the formula for the area of a triangle given its base and height:

Step 1: Identify the base and the height of the triangle from the given information.
Step 2: Apply the triangle area formula.
Step 3: Calculate the area using these values.

Now, let's apply these steps:

Step 1: From the given problem, we know:
- The base $BC$ of the triangle is $4$ units.
- The height $AE$ , which is perpendicular to $BC$ , is $8.5$ units.

Step 2: Use the formula for the area of the triangle:
$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

Step 3: Substitute the values into the formula:
$\text{Area} = \frac{1}{2} \times 4 \times 8.5 = 2 \times 8.5 = 17$

Hence, the area of the triangle is 17 square units.

3

Final Answer

17

Key Points to Remember

Essential concepts to master this topic

Formula: Area = $\frac{1}{2} \times \text{base} \times \text{height}$
Technique: Multiply base 4 by height 8.5, then divide by 2
Check: Verify 17 = (4 × 8.5) ÷ 2 = 34 ÷ 2 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to divide by 2 in the area formula
Don't just multiply base × height = 4 × 8.5 = 34! This gives you the area of a rectangle, not a triangle. The triangle is exactly half the rectangle's area. Always use the complete formula: Area = $\frac{1}{2} \times \text{base} \times \text{height}$ .

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 do we divide by 2 in the triangle area formula?

+

A triangle is exactly half of a rectangle! If you draw a rectangle with the same base and height, the triangle takes up only half that space. That's why we multiply by $\frac{1}{2}$ or divide by 2.

How do I identify the base and height from the diagram?

+

The base is any side of the triangle (here it's BC = 4). The height is the perpendicular line from the opposite vertex to that base (here it's AE = 8.5). Look for the right angle symbol!

Can I use a different side as the base?

+

Absolutely! You can choose any side as the base. Just make sure to use the perpendicular height to that base. Different base-height pairs will give the same area.

What if the height is given as a decimal like 8.5?

+

Decimal heights are perfectly fine! Just multiply as normal: $\frac{1}{2} \times 4 \times 8.5 = 2 \times 8.5 = 17$ . The calculation works the same way.

How can I check if my triangle area is reasonable?

+

The area should be less than base × height (the rectangle area)
For this problem: 17 < 34 ✓
The area should be a positive number

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Triangle Area Calculation: Finding Area with Base 4 and Height 8.5

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