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

Can a triangle have a right angle?

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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