Triangle Area Calculation: Finding ADC Area with Given Segments (15cm, 13cm, 5cm)

Q: How do I know which sides to use for the area formula?

You need a base and its perpendicular height. In this problem, AD is perpendicular to the base line, making it the perfect height for base DC or any segment on that line.

Q: Why is AD = 12 considered the height?

From the diagram, AD forms a 90-degree angle with the base line. This makes AD the perpendicular distance (height) we need for the area formula $ \frac{1}{2} \times \text{base} \times \text{height} $.

Q: What if I calculated AD differently and got a different answer?

Check your perimeter calculation! Triangle ABD has perimeter 36, so: AD + AB + BD = 36. Since AB = 15 and BD = DC + CB = 5 + 4 = 9, we get AD = 36 - 15 - 9 = 12.

Q: Can I use a different base for triangle ADC?

Yes! You could use AC as the base, but then you'd need to find the perpendicular height from D to line AC, which is more complex. Using DC = 5 as the base with height AD = 12 is the simplest approach.

Q: How do I verify my area answer is correct?

Double-check your setup: Area of triangle ADC = $ \frac{1}{2} \times DC \times AD = \frac{1}{2} \times 5 \times 12 = 30 \text{ cm}^2 $. The units should be square centimeters since we're finding area!

Triangle Area with Right Angle Properties

The perimeter of the triangle ABD shown below is 36 cm.

Given in cm:

AB = 15

AC = 13

DC = 5

CB = 4

Calculate the area of triangle ADC.

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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 ADC

00:02 Side DB equals the sum of its parts (DC+CB)

00:10 Substitute in the relevant values

00:14 Calculate the length of the side DB

00:20 The perimeter of triangle ABD equals the sum of its sides

00:32 Substitute in the relevant values

00:40 Calculate the height (AD)

00:45 Isolate AD

00:56 This is the height value (AD)

01:06 Apply the formula for calculating the area of a triangle

01:09 (height(AD) x base(DC)) divided by 2

01:14 Substitute in the relevant values

01:18 Calculate and solve

01:23 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The perimeter of the triangle ABD shown below is 36 cm.

Given in cm:

AB = 15

AC = 13

DC = 5

CB = 4

Calculate the area of triangle ADC.

Step-by-step solution

Using the given data of the triangle's perimeter we will first find the side AD by calculating the sum of all the sides of the triangle:

$AD+9+15=36$

$AD+24=36$

$AD=36-24=12$

Now that we know that AD is equal to 12, we are able to deduce that AD is also the height from BD since it forms a 90-degree angle.

If AD is the height from BD, it is also the height from DC.

Now we can calculate the area of the triangle ADC:

$\frac{AD\times DC}{2}$

$\frac{12\times5}{2}=\frac{60}{2}=30$

Final Answer

30 cm²

Key Points to Remember

Essential concepts to master this topic

Perimeter Rule: Sum all triangle sides to find unknown lengths
Technique: Use perpendicular height: $AD = 12$ forms 90° with base
Check: Area formula: $\frac{12 \times 5}{2} = 30 \text{ cm}^2$ ✓

Common Mistakes

Avoid these frequent errors

Using wrong base-height pair for area calculation
Don't use any two sides like AB and AC for area = wrong triangle and wrong answer! These aren't perpendicular to each other. Always identify the perpendicular height to your chosen base, like AD perpendicular to DC.

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 know which sides to use for the area formula?

You need a base and its perpendicular height. In this problem, AD is perpendicular to the base line, making it the perfect height for base DC or any segment on that line.

Why is AD = 12 considered the height?

From the diagram, AD forms a 90-degree angle with the base line. This makes AD the perpendicular distance (height) we need for the area formula $\frac{1}{2} \times \text{base} \times \text{height}$ .

What if I calculated AD differently and got a different answer?

Check your perimeter calculation! Triangle ABD has perimeter 36, so: AD + AB + BD = 36. Since AB = 15 and BD = DC + CB = 5 + 4 = 9, we get AD = 36 - 15 - 9 = 12.

Can I use a different base for triangle ADC?

Yes! You could use AC as the base, but then you'd need to find the perpendicular height from D to line AC, which is more complex. Using DC = 5 as the base with height AD = 12 is the simplest approach.

How do I verify my area answer is correct?

Double-check your setup: Area of triangle ADC = $\frac{1}{2} \times DC \times AD = \frac{1}{2} \times 5 \times 12 = 30 \text{ cm}^2$ . The units should be square centimeters since we're finding area!

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Triangle Area Calculation: Finding ADC Area with Given Segments (15cm, 13cm, 5cm)

Triangle Area with Right Angle Properties

❤️ 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

How do I know which sides to use for the area formula?

Why is AD = 12 considered the height?

What if I calculated AD differently and got a different answer?

Can I use a different base for triangle ADC?

How do I verify my area answer is correct?

🌟 Unlock Your Math Potential

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