Calculate Triangle Area: Right Triangle with Height 10 and Base 8

Q: What's the difference between height and the sides of the triangle?

The height is the perpendicular distance from a vertex to the opposite side. The sides (like AB or AC) are slanted and longer than the height. Only use the perpendicular height in the area formula!

Q: How do I know which line is the height?

Look for the line that forms a right angle (90°) with the base. In this problem, line AE is perpendicular to base BC, making AE the height.

Q: Why do we multiply by 1/2 in the area formula?

A triangle is half of a rectangle! If you draw a rectangle with the same base and height, the triangle takes up exactly half the space.

Q: Can I use any side as the base?

Yes! You can use any side as the base, but then you must use the perpendicular height to that chosen base. The area will be the same no matter which side you pick as the base.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the area of the triangle

00:03 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

00:22 This is 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 follow these steps:

Step 1: Identify the given dimensions: the base $BC = 8$ units, and the height $AE = 10$ units.
Step 2: Apply the triangle area formula: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ .
Step 3: Perform the calculations using the identified dimensions.

Now, let's work through each step:

Step 1: We have the base $BC = 8$ units and the height from $A$ to $BC$ , which is $AE = 10$ units.

Step 2: Using the formula for the area of a triangle, we write:

\text{Area} = \frac{1}{2} \times 8 \times 10

Step 3: Plugging in our values, we calculate:

\text{Area} = \frac{1}{2} \times 80 = 40

Therefore, the area of the triangle is 40 square units.

3

Final Answer

40

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals one-half times base times height
Technique: Use $\text{Area} = \frac{1}{2} \times 8 \times 10 = 40$
Check: Height must be perpendicular to base for correct calculation ✓

Common Mistakes

Avoid these frequent errors

Using slanted side length instead of perpendicular height
Don't use the slanted sides AB or AC as height = wrong calculation! The height must be the perpendicular distance from vertex A to base BC. Always identify the perpendicular height (AE = 10) that forms a right angle with the base.

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

What's the difference between height and the sides of the triangle?

+

The height is the perpendicular distance from a vertex to the opposite side. The sides (like AB or AC) are slanted and longer than the height. Only use the perpendicular height in the area formula!

How do I know which line is the height?

+

Look for the line that forms a right angle (90°) with the base. In this problem, line AE is perpendicular to base BC, making AE the height.

Why do we multiply by 1/2 in the area formula?

+

A triangle is half of a rectangle! If you draw a rectangle with the same base and height, the triangle takes up exactly half the space.

Can I use any side as the base?

+

Yes! You can use any side as the base, but then you must use the perpendicular height to that chosen base. The area will be the same no matter which side you pick as the base.

What if I get a decimal answer?

+

That's perfectly normal! Many triangles have decimal areas. Just make sure to show your work clearly and double-check your multiplication.

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Calculate Triangle Area: Right Triangle with Height 10 and Base 8

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