Calculate Triangle Area: Right Triangle with Base 3.5 and Height 4.6

Q: Why don't I use the hypotenuse (5.966) in the area formula?

The area formula $ A = \frac{1}{2} \times \text{base} \times \text{height} $ only needs the two perpendicular sides. The hypotenuse is the longest side but isn't used for area calculations - only for finding missing sides or perimeter!

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

In a right triangle, the base and height are the two sides that form the 90° angle. They're perpendicular to each other. The small square symbol in the corner shows you the right angle!

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

No, it doesn't matter! Since multiplication is commutative, $ 3.5 \times 4.6 = 4.6 \times 3.5 $. You'll get the same area either way.

Q: What units should my answer be in?

Since we're calculating area, your answer should be in square units. If the sides were in centimeters, your answer would be in square centimeters (cm²).

Q: Can I calculate the area without the right angle symbol?

You need to know it's a right triangle to use this formula! For other triangles, you'd need different formulas. The right angle symbol or being told it's a right triangle is essential.

Q: Why do I divide by 2 in the formula?

Think of the triangle as half of a rectangle! If you drew a rectangle with the same base and height, the triangle would be exactly half that area. That's why we multiply by $ \frac{1}{2} $.

Right Triangle Area with Given Dimensions

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

00:00 Calculate the area of the triangle

00:03 Apply the formula for calculating triangle area

00:06 (base x height) divided by 2

00:10 Substitute in the relevant values according to the given data and proceed to solve for the area

00:16 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, follow these steps:

Step 1: Identify the base $AB$ and height $AC$ of the triangle.
Step 2: Apply the formula for the area of a right triangle.
Step 3: Calculate the area using the given measurements.

Now, let's proceed:

Step 1: From the problem, the base $AB = 3.5$ units, and the height $AC = 4.6$ units.
Step 2: The area $A$ of a right triangle is given by the formula:
$A = \frac{1}{2} \times \text{base} \times \text{height}$

Step 3: Plug in the values:
$A = \frac{1}{2} \times 3.5 \times 4.6$
$A = \frac{1}{2} \times 16.1$
$A = 8.05$

Therefore, the area of the triangle is $\textbf{8.05}$ square units.

Final Answer

8.05

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals one-half times base times height
Technique: $A = \frac{1}{2} \times 3.5 \times 4.6 = 8.05$
Check: Multiply base and height first: 3.5 × 4.6 = 16.1, then divide by 2 ✓

Common Mistakes

Avoid these frequent errors

Using the hypotenuse instead of base and height
Don't use the hypotenuse 5.966 in the area formula = wrong calculation! The hypotenuse is not needed for area - it's used for perimeter or other calculations. Always identify the two perpendicular sides (base and height) for the area formula.

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

Why don't I use the hypotenuse (5.966) in the area formula?

The area formula $A = \frac{1}{2} \times \text{base} \times \text{height}$ only needs the two perpendicular sides. The hypotenuse is the longest side but isn't used for area calculations - only for finding missing sides or perimeter!

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

In a right triangle, the base and height are the two sides that form the 90° angle. They're perpendicular to each other. The small square symbol in the corner shows you the right angle!

Does it matter which side I call the base and which I call the height?

No, it doesn't matter! Since multiplication is commutative, $3.5 \times 4.6 = 4.6 \times 3.5$ . You'll get the same area either way.

What units should my answer be in?

Since we're calculating area, your answer should be in square units. If the sides were in centimeters, your answer would be in square centimeters (cm²).

Can I calculate the area without the right angle symbol?

You need to know it's a right triangle to use this formula! For other triangles, you'd need different formulas. The right angle symbol or being told it's a right triangle is essential.

Why do I divide by 2 in the formula?

Think of the triangle as half of a rectangle! If you drew a rectangle with the same base and height, the triangle would be exactly half that area. That's why we multiply by $\frac{1}{2}$ .

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