Calculate Right Triangle Area: Finding Space with Base 6 and Height 8

Q: How do I know which sides are the base and height?

Look for the right angle symbol in the diagram! The two sides that meet at the right angle are your base and height. In this triangle, AB (8) and BC (6) meet at the right angle.

Q: Does it matter which side I call base vs height?

Not at all! You can call either perpendicular side the base or height. The formula $ \frac{base \times height}{2} $ gives the same result either way: 8×6÷2 = 6×8÷2 = 24.

Q: Why don't I use the hypotenuse (side AC = 10)?

The hypotenuse is the longest side opposite the right angle. It's not perpendicular to any other side, so it can't be used as base or height in the area formula.

Q: How can I double-check my area calculation?

Substitute back into the formula: $ \frac{8 \times 6}{2} = \frac{48}{2} = 24 $. Also, the area should be less than base×height (which would be 48 for a rectangle).

Triangle Area with Base and Height

Calculate the area of the right triangle below:

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Understand the problem

Calculate the area of the right triangle below:

Step-by-step solution

Due to the fact that AB is perpendicular to BC and forms a 90-degree angle,

it can be argued that AB is the height of the triangle.

Hence we can calculate the area as follows:

$\frac{AB\times BC}{2}=\frac{8\times6}{2}=\frac{48}{2}=24$

Final Answer

24 cm²

Key Points to Remember

Essential concepts to master this topic

Formula: Area = (base × height) ÷ 2 for right triangles
Technique: Identify perpendicular sides: AB (height 8) and BC (base 6)
Check: Verify right angle exists where perpendicular sides meet ✓

Common Mistakes

Avoid these frequent errors

Using the hypotenuse as base or height
Don't use the hypotenuse (side AC = 10) in area formula = wrong answer like 40! The hypotenuse is never used in area calculations. Always identify the two perpendicular sides that form the right angle.

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 are the base and height?

Look for the right angle symbol in the diagram! The two sides that meet at the right angle are your base and height. In this triangle, AB (8) and BC (6) meet at the right angle.

Does it matter which side I call base vs height?

Not at all! You can call either perpendicular side the base or height. The formula $\frac{base \times height}{2}$ gives the same result either way: 8×6÷2 = 6×8÷2 = 24.

Why don't I use the hypotenuse (side AC = 10)?

The hypotenuse is the longest side opposite the right angle. It's not perpendicular to any other side, so it can't be used as base or height in the area formula.

What if the triangle doesn't look like it's sitting on a base?

Triangle orientation doesn't matter! Whether it's rotated or flipped, just find the two sides that form the 90-degree angle. Those are always your base and height.

How can I double-check my area calculation?

Substitute back into the formula: $\frac{8 \times 6}{2} = \frac{48}{2} = 24$ . Also, the area should be less than base×height (which would be 48 for a rectangle).

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