Calculate Triangle Area: Using Base 10 and Height 2

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

Any side can be the base, but once you choose it, the height must be the perpendicular distance from the opposite vertex to that base. In this problem, the horizontal side (length 10) is clearly the base.

Q: What does perpendicular height mean?

Perpendicular height means the straight line distance from the top vertex down to the base at a 90-degree angle. Look for the small square symbol showing the right angle in the diagram!

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

A triangle is exactly half of a rectangle! If you draw a rectangle with the same base and height, the triangle takes up exactly half that space, so we multiply by $ \frac{1}{2} $.

Q: Can I use a different formula for triangle area?

Yes! There are other formulas like Heron's formula when you know all three sides, but $ \frac{1}{2} \times \text{base} \times \text{height} $ is the simplest when you have a clear base and height.

Triangle Area with Base-Height Formula

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

00:05 Let's find the area of this triangle.

00:08 Multiply the height by the base, then divide by 2.

00:11 That's how we use the formula to calculate the area of a triangle.

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 solve the problem of finding the area of triangle $\triangle ABC$ , we follow these steps:

Step 1: Identify the given measurements.
Step 2: Use the appropriate formula for the area of a triangle.
Step 3: Calculate the area using these measurements.

Let's go through each step in detail:
Step 1: From the figure, the base $AB = 10$ and height $AC = 2$ .
Step 2: The formula for the area of a triangle is: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ .
Step 3: Substituting the known values into the formula, we get:

$\text{Area} = \frac{1}{2} \times 10 \times 2 = \frac{1}{2} \times 20 = 10$

Therefore, the area of triangle $\triangle ABC$ is 10.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals one-half times base times height
Technique: Area = $\frac{1}{2} \times 10 \times 2 = 10$
Check: Verify measurements from diagram: base = 10, height = 2 ✓

Common Mistakes

Avoid these frequent errors

Using wrong measurements as base and height
Don't multiply any two sides together = wrong area! The height must be perpendicular to the base, not just any side length. Always identify the base and the perpendicular height from the diagram.

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

How do I know which side is the base?

Any side can be the base, but once you choose it, the height must be the perpendicular distance from the opposite vertex to that base. In this problem, the horizontal side (length 10) is clearly the base.

What does perpendicular height mean?

Perpendicular height means the straight line distance from the top vertex down to the base at a 90-degree angle. Look for the small square symbol showing the right angle in the diagram!

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

A triangle is exactly half of a rectangle! If you draw a rectangle with the same base and height, the triangle takes up exactly half that space, so we multiply by $\frac{1}{2}$ .

What if I get a decimal answer?

Decimal answers are perfectly fine! Just make sure you've done the calculation correctly. In this case: $\frac{1}{2} \times 10 \times 2 = \frac{20}{2} = 10$ (a whole number).

Can I use a different formula for triangle area?

Yes! There are other formulas like Heron's formula when you know all three sides, but $\frac{1}{2} \times \text{base} \times \text{height}$ is the simplest when you have a clear base and height.

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