Calculate Triangle Area: Right Triangle with Base 10 and Height 9

Q: How do I identify which sides are the base and height?

In a right triangle, the base and height are the two perpendicular sides that meet at the right angle (the legs). The diagonal side is the hypotenuse and is never used in the area formula.

Q: Why do we multiply by ½ in the area formula?

A triangle is exactly half of a rectangle! If you drew a rectangle with the same base and height (10 × 9 = 90), the triangle would be half that area: 90 ÷ 2 = 45.

Q: Does it matter which leg I call base and which I call height?

No, it doesn't matter! You can use either perpendicular side as base or height. The formula $ \frac{1}{2} \times 9 \times 10 $ gives the same result as $ \frac{1}{2} \times 10 \times 9 $.

Q: What if I accidentally calculated 10 × 9 = 90 without the ½?

You found the area of a rectangle, not a triangle! Remember that a triangle is always half the area of a rectangle with the same dimensions. Always divide by 2.

Triangle Area with Base-Height Formula

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

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the area of the triangle

00:02 Apply the formula for calculating triangle area

00:04 (base x height) divided by 2

00:07 Substitute in the relevant values according to the given data and proceed to solve to find the area

00:10 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 solve this problem, we'll follow these steps:

Step 1: Identify the given information
Step 2: Apply the appropriate formula
Step 3: Perform the necessary calculations

Now, let's work through each step:

Step 1: We are given that $AC = 9$ (the height) and $BC = 10$ (the base) of the triangle.

Step 2: We'll use the formula for the area of a triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ .

Step 3: Plugging in our values, we have:

\text{Area} = \frac{1}{2} \times 10 \times 9 = \frac{1}{2} \times 90 = 45.

Therefore, the area of the triangle is $45$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals one-half times base times height
Technique: Identify perpendicular sides: base = 10, height = 9
Check: Area = ½ × 10 × 9 = 45 square units ✓

Common Mistakes

Avoid these frequent errors

Using the hypotenuse as base or height
Don't use the diagonal side AB = √181 in the area formula = wrong answer like 90! The hypotenuse is neither base nor height in a right triangle. Always use the two perpendicular sides (legs) that form the right angle.

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 identify which sides are the base and height?

In a right triangle, the base and height are the two perpendicular sides that meet at the right angle (the legs). The diagonal side is the hypotenuse and is never used in the area formula.

Why do we multiply by ½ in the area formula?

A triangle is exactly half of a rectangle! If you drew a rectangle with the same base and height (10 × 9 = 90), the triangle would be half that area: 90 ÷ 2 = 45.

Does it matter which leg I call base and which I call height?

No, it doesn't matter! You can use either perpendicular side as base or height. The formula $\frac{1}{2} \times 9 \times 10$ gives the same result as $\frac{1}{2} \times 10 \times 9$ .

What if I accidentally calculated 10 × 9 = 90 without the ½?

You found the area of a rectangle, not a triangle! Remember that a triangle is always half the area of a rectangle with the same dimensions. Always divide by 2.

How can I double-check my answer of 45?

Draw or imagine the triangle sitting inside a 10 × 9 rectangle. The triangle should take up exactly half the space of that rectangle. Since 90 ÷ 2 = 45, your answer is correct!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Triangle questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime