Triangle Area with 5/8 Ratio: Calculate Using 16-Unit Height

Q: Why is BC the base and not AE?

In this triangle, AE represents the height - it's the perpendicular distance from vertex A to the base. BC is the base because it's the side that the height line drops onto perpendicularly.

Q: How do I calculate BC when given the ratio?

Multiply the fraction by the known length: $ BC = \frac{5}{8} \times AE = \frac{5}{8} \times 16 = \frac{80}{8} = 10 $. Always simplify your fraction!

Q: What if I get a different area using AC as the base?

You would need the perpendicular height to side AC, which isn't given. The problem provides AE as the height, which is perpendicular to BC. Always use the base-height pair that's given!

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

A triangle is half of a rectangle with the same base and height. The rectangle would have area = base × height, so the triangle has area = $ \frac{1}{2} $ × base × height.

Triangle Area with Fraction-Based Side Ratios

Since the side BC is $\frac{5}{8}$ side AE.

Calculate the area of the triangle:

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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

00:05 BC equals five-eighths of AE according to the given data

00:08 Substitute in the value of AE in order to determine BC

00:11 Divide 16 by 8 and obtain 2

00:18 Apply the formula to calculate the triangle's area

00:22 (Base(BC) x height(AE)) divided by 2

00:27 Substitute in the relevant values and calculate to determine the area

00:31 Divide 16 by 2 and obtain 8

00:38 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Since the side BC is $\frac{5}{8}$ side AE.

Calculate the area of the triangle:

Step-by-step solution

To solve this problem, let's proceed step-by-step:

Step 1: Calculate the length of $BC$
Given $BC = \frac{5}{8} \times AE$ and $AE = 16$ , calculate:

$BC = \frac{5}{8} \times 16 = \frac{80}{8} = 10$

Step 2: Use the triangle area formula $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ .
Substitute $BC = 10$ as the base and $AE = 16$ as the height:

$\text{Area} = \frac{1}{2} \times 10 \times 16$

Step 3: Perform the calculation:

$\text{Area} = \frac{1}{2} \times 160 = 80$

Therefore, the area of triangle $\triangle ABC$ is $\boxed{80}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Triangle area equals one-half times base times height
Technique: Calculate $\frac{5}{8} \times 16 = 10$ for base BC
Check: Area = $\frac{1}{2} \times 10 \times 16 = 80$ ✓

Common Mistakes

Avoid these frequent errors

Confusing which dimension to use as base and height
Don't use AE as the base and BC as the height = area of 40! The perpendicular height AE (16 units) must pair with the horizontal base BC. Always identify the base as the side the height drops onto perpendicularly.

Practice Quiz

Test your knowledge with interactive questions

Complete the sentence:

To find the area of a right triangle, one must multiply ________________ by each other and divide by 2.

FAQ

Everything you need to know about this question

Why is BC the base and not AE?

In this triangle, AE represents the height - it's the perpendicular distance from vertex A to the base. BC is the base because it's the side that the height line drops onto perpendicularly.

How do I calculate BC when given the ratio?

Multiply the fraction by the known length: $BC = \frac{5}{8} \times AE = \frac{5}{8} \times 16 = \frac{80}{8} = 10$ . Always simplify your fraction!

What if I get a different area using AC as the base?

You would need the perpendicular height to side AC, which isn't given. The problem provides AE as the height, which is perpendicular to BC. Always use the base-height pair that's given!

Can I use the formula Area = (1/2) × side₁ × side₂ × sin(angle)?

Yes, but you'd need the angle between two sides. Since the problem gives you a clear base and height, use the simpler formula: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

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

A triangle is half of a rectangle with the same base and height. The rectangle would have area = base × height, so the triangle has area = $\frac{1}{2}$ × base × height.

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Triangle Area with 5/8 Ratio: Calculate Using 16-Unit Height

Triangle Area with Fraction-Based Side Ratios

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why is BC the base and not AE?

How do I calculate BC when given the ratio?

What if I get a different area using AC as the base?

Can I use the formula Area = (1/2) × side₁ × side₂ × sin(angle)?

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

🌟 Unlock Your Math Potential

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