Triangle Area Calculation: Can We Find Area with BC=5cm and AD=4cm?

Q: Why can't I just use Area = ½ × base × height with BC = 5 and AD = 4?

You can only use this formula when AD is perpendicular to BC. The diagram doesn't show a right angle symbol, so we can't assume AD is the height. Point D could be anywhere along BC.

Q: What information would I need to calculate the area?

You need one of these combinations:Base and height: BC = 5 cm and the perpendicular distance from A to BCAll three sides: AB, BC, and AC lengthsTwo sides and included angle: Like AB, AC, and angle BAC

Q: Could AD be a median or angle bisector instead of a height?

Possibly! But knowing AD is a median or angle bisector still doesn't give us enough information to calculate the area. We'd need additional measurements or angle information.

Q: How can I tell when I have enough information for area calculations?

Before starting any area calculation, check your given information against the three main area methods. If you can't clearly apply one of them, you likely need more data.

Triangle Area Calculation with Insufficient Information

Triangle ABC is shown below.

BC is equal to 5 cm.
Side AD is equal to 4 cm.

Is it possible to calculate the area of the triangle? If so, what is it?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine whether we are able to calculate the area of the triangle? And if so, what is it?

00:05 Apply the formula for calculating the area of a triangle

00:08 (Base(CB) x height (H)) divided by 2

00:16 We know CB but not H

00:22 Therefore, we cannot calculate the area

00:29 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Triangle ABC is shown below.

BC is equal to 5 cm.
Side AD is equal to 4 cm.

Is it possible to calculate the area of the triangle? If so, what is it?

Step-by-step solution

To determine whether it's possible to calculate the area of triangle $ABC$ with the given side $BC = 5$ cm and segment $AD = 4$ cm, we need more information than currently provided.

The possibilities for calculating the area of a triangle generally rely on knowing:

the base and the corresponding height
all three sides
two sides and the included angle

In this problem, we lack sufficient data to directly apply any of these methods. Specifically:

We do not know if $AD$ is perpendicular to $BC$ , which would make it a height usable in the base-height formula.
We only know one full side, $BC$ , and a segment, $AD$ , but no additional sides or angles.
Without confirmation that $AD$ serves as an altitude or precise geometric location or measurements of angle $\angle BAC$ , further calculations can't proceed.

Thus, with the given information, we cannot conclusively determine the area of triangle $ABC$ .

Therefore, the solution to the problem is it is not possible.

Final Answer

It is not possible.

Key Points to Remember

Essential concepts to master this topic

Area Formula Requirements: Need base-height, all sides, or two sides with included angle
Height Recognition: $AD = 4$ cm is not confirmed perpendicular to $BC$
Information Check: Always verify you have complete data before calculating area ✓

Common Mistakes

Avoid these frequent errors

Assuming AD is the height to BC
Don't assume $AD = 4$ cm is perpendicular to $BC = 5$ cm and calculate area as $\frac{1}{2} \times 5 \times 4 = 10$ cm²! Point D could be anywhere on BC without being perpendicular. Always confirm that a line segment is actually a height before using the base-height formula.

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

Why can't I just use Area = ½ × base × height with BC = 5 and AD = 4?

You can only use this formula when AD is perpendicular to BC. The diagram doesn't show a right angle symbol, so we can't assume AD is the height. Point D could be anywhere along BC.

What information would I need to calculate the area?

You need one of these combinations:

Base and height: BC = 5 cm and the perpendicular distance from A to BC
All three sides: AB, BC, and AC lengths
Two sides and included angle: Like AB, AC, and angle BAC

Could AD be a median or angle bisector instead of a height?

Possibly! But knowing AD is a median or angle bisector still doesn't give us enough information to calculate the area. We'd need additional measurements or angle information.

How can I tell when I have enough information for area calculations?

Before starting any area calculation, check your given information against the three main area methods. If you can't clearly apply one of them, you likely need more data.

What if the problem said 'AD is perpendicular to BC'?

Then you could calculate the area! With AD ⊥ BC, you'd have base = BC = 5 cm and height = AD = 4 cm, giving Area = $\frac{1}{2} \times 5 \times 4 = 10$ cm².

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Triangle Area Calculation: Can We Find Area with BC=5cm and AD=4cm?

Triangle Area Calculation with Insufficient Information

❤️ 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 can't I just use Area = ½ × base × height with BC = 5 and AD = 4?

What information would I need to calculate the area?

Could AD be a median or angle bisector instead of a height?

How can I tell when I have enough information for area calculations?

What if the problem said 'AD is perpendicular to BC'?

🌟 Unlock Your Math Potential

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