Triangle Area Calculation: Finding Area with Base 5 and Height 6

Q: Why can't I use the side length of 9 as the height?

The height must be perpendicular to the base! Side length 9 is slanted, not at a 90° angle to the base. Only the vertical line marked as 6 forms a right angle with the base.

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

Look for the dashed or dotted line that forms a right angle (90°) with one side. In this triangle, the vertical line of length 6 is perpendicular to the horizontal base of length 5.

Q: Does it matter which side I choose as the base?

No! You can choose any side as the base, but you must use the perpendicular height to that base. Different base-height pairs will give the same area.

Q: What if the triangle looks different but has the same measurements?

The area formula works for all triangles! Whether it's right, acute, or obtuse, as long as you have a base and its perpendicular height, use Area = (base × height) ÷ 2.

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

A triangle is half of a rectangle! If you imagine completing the rectangle using the same base and height, the triangle takes up exactly half that space.

Triangle Area with Base-Height Method

What is the area of the given triangle?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine the area of the triangle

00:03 In order to calculate the triangle's area we will utilize the following formula

00:06 (Base x height) divided by 2

00:11 Insert the known data into the formula as follows (base(5) x height(6)) divided by 2

00:16 Proceed to calculate

00:22 Here is the solution

Step-by-step written solution

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Understand the problem

What is the area of the given triangle?

Step-by-step solution

This question is a bit confusing. We need start by identifying which parts of the data are relevant to us.

Remember the formula for the area of a triangle:

A1- How to find the area of a triangle The height is a straight line that comes out of an angle and forms a right angle with the opposite side.

In the drawing we have a height of 6.

It goes down to the opposite side whose length is 5.

And therefore, these are the data points that we will use.

We replace in the formula:

$\frac{6\times5}{2}=\frac{30}{2}=15$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area = (base × height) ÷ 2 for any triangle
Technique: Use perpendicular height: (5 × 6) ÷ 2 = 15
Check: Height must be perpendicular to base you choose ✓

Common Mistakes

Avoid these frequent errors

Using the wrong side as height
Don't use side length 9 as height = Area of 22.5 instead of 15! The height must be perpendicular (90°) to the base, not just any side length. Always identify the perpendicular line from vertex to opposite side.

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 the side length of 9 as the height?

The height must be perpendicular to the base! Side length 9 is slanted, not at a 90° angle to the base. Only the vertical line marked as 6 forms a right angle with the base.

How do I know which line is the height?

Look for the dashed or dotted line that forms a right angle (90°) with one side. In this triangle, the vertical line of length 6 is perpendicular to the horizontal base of length 5.

Does it matter which side I choose as the base?

No! You can choose any side as the base, but you must use the perpendicular height to that base. Different base-height pairs will give the same area.

What if the triangle looks different but has the same measurements?

The area formula works for all triangles! Whether it's right, acute, or obtuse, as long as you have a base and its perpendicular height, use Area = (base × height) ÷ 2.

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

A triangle is half of a rectangle! If you imagine completing the rectangle using the same base and height, the triangle takes up exactly half that space.

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