Calculate Triangle Area: Using Height 8 and Base 11

Q: Why do we multiply by one-half in the triangle area formula?

A triangle is half of a rectangle! If you draw a rectangle with the same base and height, the triangle would be exactly half its area. That's why we need the $ \frac{1}{2} $ factor.

Q: What if the height isn't drawn inside the triangle?

The height can be outside the triangle in obtuse triangles! As long as it's perpendicular to the base (makes a 90° angle), the formula still works perfectly.

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

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

Q: What does perpendicular mean exactly?

Perpendicular means the height line makes a perfect 90-degree angle with the base. Look for the small square symbol (⊥) that shows this right angle in diagrams.

Q: Can I use this formula for any triangle?

Yes! This formula works for all triangles - acute, right, and obtuse. As long as you have a base and its corresponding perpendicular height, you're set!

Triangle Area with Base-Height Formula

AD is the height of triangle ABC.

BC = 11

AD = 8

Calculate the area of the 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

00:03 Apply the formula for calculating the area of a triangle

00:07 (base x height) ➗ 2

00:12 Substitute in the relevant values according to the given data and proceed to solve for the area

00:36 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

AD is the height of triangle ABC.

BC = 11

AD = 8

Calculate the area of the triangle.

Step-by-step solution

To solve for the area of triangle $\triangle ABC$ , we will use the standard formula for the area of a triangle:

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

Given:
Base $BC = 11$
Height $AD = 8$

Substitute these values into the area formula:

$\text{Area} = \frac{1}{2} \times 11 \times 8$

Calculate the area:

$\text{Area} = \frac{1}{2} \times 88 = 44$

Therefore, the area of triangle $\triangle ABC$ is $\boxed{44}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area = $\frac{1}{2} \times \text{base} \times \text{height}$
Calculation: $\frac{1}{2} \times 11 \times 8 = 44$ square units
Check: Height is perpendicular to base, making a right angle ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by one-half
Don't calculate base × height = 11 × 8 = 88 and call that your area! This gives double the correct answer because you skipped the ½ factor. Always use the complete formula: Area = ½ × base × height.

Practice Quiz

Test your knowledge with interactive questions

Is the straight line in the figure the height of the triangle?

FAQ

Everything you need to know about this question

Why do we multiply by one-half in the triangle area formula?

A triangle is half of a rectangle! If you draw a rectangle with the same base and height, the triangle would be exactly half its area. That's why we need the $\frac{1}{2}$ factor.

What if the height isn't drawn inside the triangle?

The height can be outside the triangle in obtuse triangles! As long as it's perpendicular to the base (makes a 90° angle), the formula still works perfectly.

How do I know which side is the base?

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

What does perpendicular mean exactly?

Perpendicular means the height line makes a perfect 90-degree angle with the base. Look for the small square symbol (⊥) that shows this right angle in diagrams.

Can I use this formula for any triangle?

Yes! This formula works for all triangles - acute, right, and obtuse. As long as you have a base and its corresponding perpendicular height, you're set!

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