Triangle Area Calculation: Finding Area with 3m Base and 2/3m Height

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

The triangle area formula $ A = \frac{1}{2} \times b \times h $ comes from the fact that a triangle is half of a rectangle. A rectangle with the same base and height would have area b × h, so the triangle has half that area.

Q: Can I multiply the fractions in a different order?

Yes! Multiplication is commutative, so you can calculate $ \frac{1}{2} \times 3 \times \frac{2}{3} $ in any order. Try $ \frac{1}{2} \times \frac{2}{3} = \frac{1}{3} $ first, then multiply by 3.

Q: How do I multiply a whole number by a fraction?

To multiply 3 by $ \frac{2}{3} $, think of 3 as $ \frac{3}{1} $. Then multiply: $ \frac{3}{1} \times \frac{2}{3} = \frac{6}{3} = 2 $. The 3's cancel out!

Q: What if my height or base is a mixed number?

Convert mixed numbers to improper fractions first! For example, if height was $ 1\frac{1}{3} $, convert it to $ \frac{4}{3} $ before using the area formula.

Q: Why is the answer 1 and not 1 meter?

The answer is 1 square meter, not just 1 meter! Area is always measured in square units because we're measuring a 2-dimensional space. Length × Length = Area in square units.

Triangle Area with Fractional Height

What is the area of a triangle whose side length is $3$ meters and its height $\frac{2}{3}$ meters?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's find the area of the triangle.

00:11 We'll use the formula: Area equals base times height, divided by two.

00:17 First, substitute the base and height with the given numbers.

00:23 Then, we'll change the whole number to a fraction.

00:30 Remember to multiply the numerators together, and multiply the denominators together.

00:35 Now, we'll simplify the fraction as much as we can.

00:45 Next, change the fraction back to a whole number if possible.

00:49 And that's the solution! We've found the area of the triangle.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the area of a triangle whose side length is $3$ meters and its height $\frac{2}{3}$ meters?

Step-by-step solution

To determine the area of the triangle, we will proceed as follows:

Identify the base and height from the problem.
Use the formula for the area of a triangle, $A = \frac{1}{2} \times b \times h$ .
Substitute the given values and compute the area.

First, the base $b$ of the triangle is $3$ meters, and the height $h$ is $\frac{2}{3}$ meters. To find the area, we will use the formula:

$A = \frac{1}{2} \times b \times h$

Substituting, we get:

$A = \frac{1}{2} \times 3 \times \frac{2}{3}$

We begin by calculating the multiplication inside the formula:

$A = \frac{1}{2} \times \left(3 \times \frac{2}{3}\right)$

Here, $3 \times \frac{2}{3} = \frac{6}{3} = 2$ .

Then, multiply by $\frac{1}{2}$ :

$A = \frac{1}{2} \times 2 = 1$ .

The area of the triangle is $1$ square meter.

The correct answer from the choices provided is: $1$ .

Final Answer

$1$

Key Points to Remember

Essential concepts to master this topic

Formula: Area of triangle equals one-half times base times height
Technique: Multiply $3 \times \frac{2}{3} = 2$ first, then multiply by $\frac{1}{2}$
Check: $\frac{1}{2} \times 3 \times \frac{2}{3} = \frac{1}{2} \times 2 = 1$ square meter ✓

Common Mistakes

Avoid these frequent errors

Adding base and height instead of multiplying
Don't add 3 + 2/3 = 3⅔! This completely ignores the area formula and gives the wrong units. Always multiply base times height, then multiply by ½ using the triangle area formula.

Practice Quiz

Test your knowledge with interactive questions

$\frac{1}{4}\times\frac{3}{2}=$

FAQ

Everything you need to know about this question

Why do I multiply by ½ in the triangle area formula?

The triangle area formula $A = \frac{1}{2} \times b \times h$ comes from the fact that a triangle is half of a rectangle. A rectangle with the same base and height would have area b × h, so the triangle has half that area.

Can I multiply the fractions in a different order?

Yes! Multiplication is commutative, so you can calculate $\frac{1}{2} \times 3 \times \frac{2}{3}$ in any order. Try $\frac{1}{2} \times \frac{2}{3} = \frac{1}{3}$ first, then multiply by 3.

How do I multiply a whole number by a fraction?

To multiply 3 by $\frac{2}{3}$ , think of 3 as $\frac{3}{1}$ . Then multiply: $\frac{3}{1} \times \frac{2}{3} = \frac{6}{3} = 2$ . The 3's cancel out!

What if my height or base is a mixed number?

Convert mixed numbers to improper fractions first! For example, if height was $1\frac{1}{3}$ , convert it to $\frac{4}{3}$ before using the area formula.

Why is the answer 1 and not 1 meter?

The answer is 1 square meter, not just 1 meter! Area is always measured in square units because we're measuring a 2-dimensional space. Length × Length = Area in square units.

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