Calculate Triangle Area: Finding Space with Base 6.5 and Height 3

Q: Why do we multiply by 1/2 for triangle area?

A triangle is exactly half of a rectangle! If you draw a rectangle with the same base and height, the triangle would fit inside it twice. That's why we use $ \frac{1}{2} $.

Q: Can I use 0.5 instead of 1/2?

Absolutely! Both $ \frac{1}{2} $ and 0.5 mean the same thing. So 0.5 × 6.5 × 3 = 9.75 gives the same answer.

Q: What if my base or height has more decimal places?

No problem! Just be careful with your decimal multiplication. Count the total decimal places in all numbers you're multiplying to place your decimal correctly in the answer.

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

The height is always perpendicular (at a 90° angle) to the base. In this problem, you can see the purple line showing height 3 is vertical, making a right angle with the green base line of 6.5.

Triangle Area Formula with Decimal Measurements

Calculate the area of the following triangle:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the triangle's area

00:02 Apply the formula for calculating the area of a triangle

00:06 (base(BC) x height(AE)) divided by 2

00:10 Substitute in the relevant values and proceed to solve

00:25 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 following triangle:

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given base and height.
Step 2: Apply the formula for the area of a triangle.
Step 3: Perform the calculation to find the area.

Now, let's work through each step:
Step 1: The base of the triangle is $6.5$ and the height is $3$ .
Step 2: We'll use the formula for the area of a triangle, given by: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ .
Step 3: Plugging in our values, we get:

$\text{Area} = \frac{1}{2} \times 6.5 \times 3 = \frac{1}{2} \times 19.5 = 9.75$

Therefore, the area of the triangle is $\boxed{9.75}$ .

Final Answer

9.75

Key Points to Remember

Essential concepts to master this topic

Formula: Area of triangle equals one-half times base times height
Technique: Calculate $\frac{1}{2} \times 6.5 \times 3 = 9.75$
Check: Verify units are squared and decimal placement is correct ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by one-half
Don't just multiply base times height (6.5 × 3 = 19.5) = double the correct area! This gives you the area of a rectangle, not a triangle. Always multiply by $\frac{1}{2}$ to get the triangle area.

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 multiply by 1/2 for triangle area?

A triangle is exactly half of a rectangle! If you draw a rectangle with the same base and height, the triangle would fit inside it twice. That's why we use $\frac{1}{2}$ .

Can I use 0.5 instead of 1/2?

Absolutely! Both $\frac{1}{2}$ and 0.5 mean the same thing. So 0.5 × 6.5 × 3 = 9.75 gives the same answer.

What if my base or height has more decimal places?

No problem! Just be careful with your decimal multiplication. Count the total decimal places in all numbers you're multiplying to place your decimal correctly in the answer.

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

The height is always perpendicular (at a 90° angle) to the base. In this problem, you can see the purple line showing height 3 is vertical, making a right angle with the green base line of 6.5.

Do I need to include units in my answer?

If the problem gives units (like cm or inches), your answer should have square units (like cm² or square inches). Since this problem doesn't specify units, just the number 9.75 is correct.

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