Calculate Triangle Area: Finding Area with Base 6 and Height 8

Q: Why do we multiply by 1/2 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 use $ \frac{1}{2} \times \text{base} \times \text{height} $.

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

The base is any side of the triangle (here it's 6). The height is the perpendicular distance from that base to the opposite vertex (here it's 8). Look for the right angle symbol!

Q: Does it matter which side I choose as the base?

No! You can use any side as the base, but then you must use the perpendicular height to that side. The area will always be the same.

Q: What if I get a different answer when I calculate?

Double-check these steps: ½ × 6 × 8. First multiply 6 × 8 = 48, then multiply by ½ to get 24. Make sure you're not forgetting the ½!

Q: Can I multiply in a different order?

Yes! You can calculate $ \frac{1}{2} \times 6 \times 8 $ in any order: (½ × 6) × 8 = 3 × 8 = 24, or ½ × (6 × 8) = ½ × 48 = 24. Both give the same answer!

Triangle Area Formula with Base and Height

Calculate the area of the triangle using the data in the figure below.

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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

00:03 Apply the formula for calculating triangle area

00:06 (base x height) divided by 2

00:10 Substitute in the relevant values according to the given data and proceed to solve for the area

00:14 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 triangle using the data in the figure below.

Step-by-step solution

To calculate the area of the triangle, we will follow these steps:

Identify the base, CB, as 6 units.
Identify the height, AC, as 8 units.
Apply the area formula for a triangle.

Now, let's work through these steps:

The triangle is a right triangle with base $CB = 6$ units and height $AC = 8$ units.

The area of a triangle is determined using the formula:

\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}

Substituting the known values, we have:

\text{Area} = \frac{1}{2} \times 6 \times 8

Perform the multiplication and division:

\text{Area} = \frac{1}{2} \times 48 = 24

Therefore, the area of the triangle is $24$ square units.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals half times base times height
Calculation: $\frac{1}{2} \times 6 \times 8 = 24$ square units
Check: Verify base is 6, height is 8, and formula gives 24 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by one-half
Don't just multiply base × height = 6 × 8 = 48! This gives the area of a rectangle, not a triangle. Always multiply by ½ first: Area = ½ × base × 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 multiply by 1/2 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 use $\frac{1}{2} \times \text{base} \times \text{height}$ .

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

The base is any side of the triangle (here it's 6). The height is the perpendicular distance from that base to the opposite vertex (here it's 8). Look for the right angle symbol!

Does it matter which side I choose as the base?

No! You can use any side as the base, but then you must use the perpendicular height to that side. The area will always be the same.

What if I get a different answer when I calculate?

Double-check these steps: ½ × 6 × 8. First multiply 6 × 8 = 48, then multiply by ½ to get 24. Make sure you're not forgetting the ½!

Can I multiply in a different order?

Yes! You can calculate $\frac{1}{2} \times 6 \times 8$ in any order: (½ × 6) × 8 = 3 × 8 = 24, or ½ × (6 × 8) = ½ × 48 = 24. Both give the same answer!

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