Calculate Triangle Area: Using Height 9 and Base 8 with Given Measurements

Q: Why can't I use all three measurements (8, 9, and 12) in the formula?

The triangle area formula only needs one base and its corresponding height. The third measurement (AB = 12) is extra information that isn't needed for this calculation.

Q: How do I know which line is the height?

The height is always the perpendicular line from a vertex to the opposite side. Look for the right angle symbol (square corner) - that shows AD is perpendicular to CB.

Q: What if I accidentally used AB = 12 as the base?

If you use AB = 12 with height AD = 9, you'd get $ \frac{12 \times 9}{2} = 54 $ cm², which is wrong! The height AD is not perpendicular to side AB.

Q: Can I use a different base and height?

You need a perpendicular height for whatever base you choose. In this diagram, we only have one height shown (AD = 9), so we must use CB = 8 as the base.

Q: Why do we divide by 2 in the triangle area formula?

A triangle is half of a rectangle with the same base and height. So we calculate the rectangle area (base × height) then divide by 2 to get the triangle area.

Triangle Area with Height and Base

Calculate the area of the triangle ABC using the data in the figure.

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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 ABC

00:02 Apply the formula for calculating the area of a triangle

00:05 (Base(CB) x height (H)) divided by 2

00:15 Mark AD as height (H)

00:24 Substitute the relevant values into our formula

00:31 Calculate and solve

00:35 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate the area of the triangle ABC using the data in the figure.

Step-by-step solution

First, let's remember the formula for the area of a triangle:

(the side * the height that descends to the side) /2

In the question, we have three pieces of data, but one of them is redundant!

We only have one height, the line that forms a 90-degree angle - AD,

The side to which the height descends is CB,

Therefore, we can use them in our calculation:

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

$\frac{8\times9}{2}=\frac{72}{2}=36$

Final Answer

36 cm²

Key Points to Remember

Essential concepts to master this topic

Formula: Area = (base × height) ÷ 2 for any triangle
Technique: Use perpendicular height AD = 9 and base CB = 8
Check: Substitute: (8 × 9) ÷ 2 = 72 ÷ 2 = 36 cm² ✓

Common Mistakes

Avoid these frequent errors

Using the wrong side as the base for the given height
Don't use side AB = 12 as the base with height AD = 9 incorrect calculation! The height must be perpendicular to the base, and AD is only perpendicular to CB. Always identify which side the height is perpendicular to before calculating.

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 use all three measurements (8, 9, and 12) in the formula?

The triangle area formula only needs one base and its corresponding height. The third measurement (AB = 12) is extra information that isn't needed for this calculation.

How do I know which line is the height?

The height is always the perpendicular line from a vertex to the opposite side. Look for the right angle symbol (square corner) - that shows AD is perpendicular to CB.

What if I accidentally used AB = 12 as the base?

If you use AB = 12 with height AD = 9, you'd get $\frac{12 \times 9}{2} = 54$ cm², which is wrong! The height AD is not perpendicular to side AB.

Can I use a different base and height?

You need a perpendicular height for whatever base you choose. In this diagram, we only have one height shown (AD = 9), so we must use CB = 8 as the base.

Why do we divide by 2 in the triangle area formula?

A triangle is half of a rectangle with the same base and height. So we calculate the rectangle area (base × height) then divide by 2 to get the triangle area.

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