Right Triangle Area Calculation: 36cm Perimeter with Given Side Lengths

Q: Why is BD equal to DC + CB instead of being separate?

Point C lies on side BD, dividing it into two segments. So BD is the total length from B to D, which equals DC + CB = 5 + 4 = 9 cm.

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

For a right triangle, use the two perpendicular sides (legs) in the formula $ \frac{base \times height}{2} $. Here, AD and BD are perpendicular, so use those!

Q: Can I solve this without finding AD first?

No! You need all three side lengths to use the perimeter information. First find AD using the perimeter, then calculate the area using AD and BD.

Q: What if I calculated the area as 30 cm²?

You likely used half the correct base. Remember BD = 9 cm (not 4 or 5), so area = $ \frac{12 \times 9}{2} = 54 $ cm², not 30 cm².

Q: Why don't we use AB = 15 cm in the area calculation?

AB = 15 cm is the hypotenuse (longest side). For area, we only use the two perpendicular sides (legs): AD = 12 cm and BD = 9 cm.

Right Triangle Area with Composite Figures

Below is the right triangle ABD, which has a perimeter of 36 cm.

AB = 15

AC = 13

DC = 5

CB = 4

Work out 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 ABD

00:03 Substitute in the relevant values according to the given data

00:15 The side (BD) equals the sum of its parts (BC+CD)

00:19 Substitute in the relevant values according to the given data

00:24 This is the length of the base (BD)

00:29 The perimeter of the triangle equals the sum of its sides

00:38 Substitute in the relevant values

00:50 Solve to obtain DA

00:53 Isolate DA

01:01 Calculate and solve

01:05 This is the length (DA)

01:11 Now we want to calculate the area of the triangle ABD

01:14 Apply the formula for calculating the area of the triangle

01:17 (Height(AD) x base(BD)) divided by 2

01:21 Substitute in the relevant values

01:25 Calculate and solve

01:33 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Below is the right triangle ABD, which has a perimeter of 36 cm.

AB = 15

AC = 13

DC = 5

CB = 4

Work out the area of the triangle.

Step-by-step solution

According to the data:

$BD=4+5=9$

Now that we are given the perimeter of triangle ABD we can find the missing side AD:

$AD+15+9=36$

$AD+24=36$

$AD=36-24=12$

Thus we can calculate the area of triangle ABD:

$\frac{AD\times BD}{2}=\frac{12\times9}{2}=\frac{108}{2}=54$

Final Answer

54 cm²

Key Points to Remember

Essential concepts to master this topic

Perimeter Rule: Add all three sides to find missing side length
Technique: BD = DC + CB = 5 + 4 = 9 cm total
Check: Verify AD + AB + BD = 12 + 15 + 9 = 36 cm ✓

Common Mistakes

Avoid these frequent errors

Using individual segments instead of total side lengths
Don't calculate area using DC = 5 and CB = 4 separately = wrong base measurement! This ignores that C lies on side BD, making BD the actual base. Always use the complete side BD = DC + CB = 9 cm as your base.

Practice Quiz

Test your knowledge with interactive questions

Find the perimeter of the triangle ABC

FAQ

Everything you need to know about this question

Why is BD equal to DC + CB instead of being separate?

Point C lies on side BD, dividing it into two segments. So BD is the total length from B to D, which equals DC + CB = 5 + 4 = 9 cm.

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

For a right triangle, use the two perpendicular sides (legs) in the formula $\frac{base \times height}{2}$ . Here, AD and BD are perpendicular, so use those!

Can I solve this without finding AD first?

No! You need all three side lengths to use the perimeter information. First find AD using the perimeter, then calculate the area using AD and BD.

What if I calculated the area as 30 cm²?

You likely used half the correct base. Remember BD = 9 cm (not 4 or 5), so area = $\frac{12 \times 9}{2} = 54$ cm², not 30 cm².

Why don't we use AB = 15 cm in the area calculation?

AB = 15 cm is the hypotenuse (longest side). For area, we only use the two perpendicular sides (legs): AD = 12 cm and BD = 9 cm.

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Right Triangle Area Calculation: 36cm Perimeter with Given Side Lengths

Right Triangle Area with Composite Figures

❤️ 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 BD equal to DC + CB instead of being separate?

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

Can I solve this without finding AD first?

What if I calculated the area as 30 cm²?

Why don't we use AB = 15 cm in the area calculation?

🌟 Unlock Your Math Potential

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