Calculate Triangle ABC Area in Cuboid with Volume 120 cm³ and Side 4 cm

Q: Why can I use the simple triangle formula here?

When triangle ABC has two sides that are perpendicular edges of the cuboid (like length and width), you can treat them as base and height. The formula $ \frac{1}{2} \times \text{base} \times \text{height} $ works perfectly!

Q: Could triangle ABC be oriented differently?

Yes! But the key insight is that triangle ABC forms a right triangle using two perpendicular edges of the cuboid. No matter how it's oriented, the area calculation using $ \frac{1}{2} \times l \times w $ remains the same.

Cuboid Volume with Triangle Area Calculation

A cuboid has a volume of

120 cm3.

Side BK equals 4 cm.

Calculate the area of the triangle ABC.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the area of triangle ABC

00:03 We'll use the formula for calculating box volume

00:07 Width multiplied by height multiplied by length

00:13 Let's substitute appropriate values and solve

00:23 We'll isolate the product of height and width

00:28 Which is actually the product of height and base in triangle ABC

00:32 We'll use the formula for calculating triangle area

00:38 (Base multiplied by height) divided by 2

00:42 Let's substitute appropriate values and solve for the area

00:49 And that's the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A cuboid has a volume of

120 cm3.

Side BK equals 4 cm.

Calculate the area of the triangle ABC.

Step-by-step solution

To solve this problem, we will derive the dimensions of the cuboid using the given volume and side BK, and then find the area of triangle ABC.

We start with the given information:
- Volume of the cuboid: $120 \, \text{cm}^3$
- Side $BK = 4 \, \text{cm}$

The volume formula of the cuboid is:
$V = l \times w \times h = 120 \, \text{cm}^3$

We assume $BK = h = 4 \, \text{cm}$ , leading to:
$l \times w \times 4 = 120$
$l \times w = \frac{120}{4} = 30$

Now, to get the area of triangle ABC, which forms a right triangle with sides $l$ and $w$ being the base and height, respectively, we use:
$A = \frac{1}{2} \times l \times w = \frac{1}{2} \times 30 = 15 \, \text{cm}^2$

Thus, the area of triangle ABC is $15 \, \text{cm}^2$ .

Final Answer

15 cm²

Key Points to Remember

Essential concepts to master this topic

Volume Formula: Use V = l × w × h to find missing dimensions
Technique: Given BK = 4 cm and V = 120 cm³, find l × w = 30
Check: Triangle area formula gives $\frac{1}{2} \times 30 = 15 \text{ cm}^2$ ✓

Common Mistakes

Avoid these frequent errors

Using triangle ABC as a face of the cuboid
Don't assume triangle ABC is on the cuboid's surface = wrong triangle entirely! The triangle is formed by connecting vertices A, B, and C in 3D space, not lying flat on a face. Always identify which triangle you're finding by looking at the vertex positions in the diagram.

Practice Quiz

Test your knowledge with interactive questions

A rectangular prism has a base measuring 5 units by 8 units.

The height of the prism is 12 units.

Calculate its volume.

FAQ

Everything you need to know about this question

How do I know which triangle ABC is in this 3D shape?

Look at the diagram carefully! Triangle ABC is formed by connecting three vertices of the cuboid. It's not necessarily on a flat face - it could be a diagonal triangle cutting through the 3D space.

Why can I use the simple triangle formula here?

When triangle ABC has two sides that are perpendicular edges of the cuboid (like length and width), you can treat them as base and height. The formula $\frac{1}{2} \times \text{base} \times \text{height}$ works perfectly!

What if I can't figure out which sides are l, w, and h?

Don't worry about labeling them specifically! Since you know BK = 4 cm and the volume is 120 cm³, you can find that the other two dimensions multiply to give 30. That's all you need for the triangle area.

Could triangle ABC be oriented differently?

Yes! But the key insight is that triangle ABC forms a right triangle using two perpendicular edges of the cuboid. No matter how it's oriented, the area calculation using $\frac{1}{2} \times l \times w$ remains the same.

How do I check if 15 cm² is reasonable?

Compare it to the cuboid's faces! If the cuboid has dimensions creating faces of 30 cm², then a triangle that's half of such an area (15 cm²) makes perfect sense. Always do a reality check with your geometry problems!

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Calculate Triangle ABC Area in Cuboid with Volume 120 cm³ and Side 4 cm

Cuboid Volume with Triangle Area Calculation

❤️ 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 triangle ABC is in this 3D shape?

Why can I use the simple triangle formula here?

What if I can't figure out which sides are l, w, and h?

Could triangle ABC be oriented differently?

How do I check if 15 cm² is reasonable?

🌟 Unlock Your Math Potential

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