Calculate Triangle Area with 1/5 Ratio: Height-Base Geometry Problem

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

Look at the diagram carefully! The height is always perpendicular (forms a 90° angle) to the base. Here, AE is drawn vertically and perpendicular to the horizontal base BC.

Q: Why do we use the ratio 1/5 to find BC?

The problem states that BC is $ \frac{1}{5} $ of side AE. Since AE = 10, we calculate: BC = 1/5 × 10 = 2. This gives us the actual length of the base.

Q: What if I calculated BC = 1/5 × 10 = 0.2 instead of 2?

Be careful with your arithmetic! $ \frac{1}{5} \times 10 = \frac{10}{5} = 2 $, not 0.2. Remember that dividing by 5 is the same as multiplying by 1/5.

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

The standard formula $ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} $ works best here because we have a clear perpendicular height. Other formulas like Heron's formula would be unnecessarily complicated.

Q: How do I check if my answer of 10 is correct?

Verify by checking the calculation: $ \text{Area} = \frac{1}{2} \times 2 \times 10 = \frac{20}{2} = 10 $. The numbers should make sense with the given ratio and measurements! ✓

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the triangle's area

00:06 BC equals one-fifth of AE according to the given data

00:12 Substitute in the value of AE in order to determine BC

00:18 Apply the formula for calculating the area of a triangle

00:21 (base(BC) x height(AE)) divided by 2

00:26 Substitute in the relevant values and calculate to determine the area

00:32 Reduce the 2

00:36 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Since the side BC is $\frac{1}{5}$ side AE.

Calculate the area of the triangle:

2

Step-by-step solution

To solve the problem, we will follow these steps:

Step 1: Using $AE = 10$ , calculate $BC$ using the information that $BC = \frac{1}{5} \times AE$ .
Step 2: Apply the formula for the area of a triangle.

We proceed with the calculations:
Step 1: Since $BC = \frac{1}{5} \times 10 = 2$ .
Step 2: Assume $AB$ is perpendicular to $BC$ to apply the formula $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ .

The triangle $\triangle ABC$ is vertical, implying that base $BC$ and height $AE$ can be used because it suggests $AE$ is perpendicular to $BC$ . Thus,
$\text{Area} = \frac{1}{2} \times AE \times BC = \frac{1}{2} \times 10 \times 2 = 10$ .

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

3

Final Answer

10

Key Points to Remember

Essential concepts to master this topic

Given Ratio: Use BC = 1/5 × AE to find base length
Height Identification: AE = 10 serves as perpendicular height to base BC
Area Verification: Check that 1/2 × 10 × 2 = 10 square units ✓

Common Mistakes

Avoid these frequent errors

Using AE as the base instead of BC
Don't use AE = 10 as the base with BC = 2 as height = Area of 1/2 × 10 × 2 calculated wrong! The perpendicular height AE should multiply with the actual base BC. Always identify which measurement is the base and which is the perpendicular height from the diagram.

Practice Quiz

Test your knowledge with interactive questions

What is the ratio between the orange and gray parts in the drawing?

FAQ

Everything you need to know about this question

How do I know which side is the base and which is the height?

+

Look at the diagram carefully! The height is always perpendicular (forms a 90° angle) to the base. Here, AE is drawn vertically and perpendicular to the horizontal base BC.

Why do we use the ratio 1/5 to find BC?

+

The problem states that BC is $\frac{1}{5}$ of side AE. Since AE = 10, we calculate: BC = 1/5 × 10 = 2. This gives us the actual length of the base.

What if I calculated BC = 1/5 × 10 = 0.2 instead of 2?

+

Be careful with your arithmetic! $\frac{1}{5} \times 10 = \frac{10}{5} = 2$ , not 0.2. Remember that dividing by 5 is the same as multiplying by 1/5.

Can I use a different formula for triangle area?

+

The standard formula $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ works best here because we have a clear perpendicular height. Other formulas like Heron's formula would be unnecessarily complicated.

How do I check if my answer of 10 is correct?

+

Verify by checking the calculation: $\text{Area} = \frac{1}{2} \times 2 \times 10 = \frac{20}{2} = 10$ . The numbers should make sense with the given ratio and measurements! ✓

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Calculate Triangle Area with 1/5 Ratio: Height-Base Geometry Problem

Triangle Area with Ratio-Based Dimensions

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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

How do I know which side is the base and which is the height?

Why do we use the ratio 1/5 to find BC?

What if I calculated BC = 1/5 × 10 = 0.2 instead of 2?

Can I use a different formula for triangle area?

How do I check if my answer of 10 is correct?

🌟 Unlock Your Math Potential

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