Calculate Triangle Area: Right Triangle with Base 6 and Height 7

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

A triangle is exactly half of a rectangle! When you multiply base × height, you get a rectangle's area. Since a triangle takes up half that space, you must divide by 2.

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

The height must be perpendicular (form a 90° angle) to the base. In this problem, the vertical line labeled '7' is perpendicular to the horizontal base labeled '6'.

Q: What if the triangle isn't a right triangle?

You can still use $ A = \frac{1}{2} \times base \times height $, but you need to find the perpendicular height - the shortest distance from the base to the opposite vertex.

Q: Can I use any side as the base?

Yes! You can choose any side as the base, but then you must use the perpendicular distance to that side as the height. The area will always be the same.

Q: What units should my answer have?

Area is always in square units. If your measurements are in centimeters, the area is in cm². If no units are given, just write the number like '21'.

Triangle Area with Right Angle Formula

Calculate the area of the following triangle:

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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

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

00:05 (base(BC) x height (AE)) divided by 2

00:10 Substitute in the relevant values and proceed to solve

00:23 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 following triangle:

Step-by-step solution

The formula for the area of a triangle is

$A = \frac{h\cdot base}{2}$

Let's insert the available data into the formula:

(7*6)/2 =

42/2 =

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals base times height divided by two
Technique: Multiply 6 × 7 = 42, then divide by 2
Check: Verify perpendicular height creates right angle at base ✓

Common Mistakes

Avoid these frequent errors

Forgetting to divide by 2
Don't just multiply base × height = 42 as final answer! This gives the area of a rectangle, not a triangle. Always divide by 2 because a triangle is exactly half the area of a rectangle.

Practice Quiz

Test your knowledge with interactive questions

Complete the sentence:

To find the area of a right triangle, one must multiply ________________ by each other and divide by 2.

FAQ

Everything you need to know about this question

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

A triangle is exactly half of a rectangle! When you multiply base × height, you get a rectangle's area. Since a triangle takes up half that space, you must divide by 2.

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

The height must be perpendicular (form a 90° angle) to the base. In this problem, the vertical line labeled '7' is perpendicular to the horizontal base labeled '6'.

What if the triangle isn't a right triangle?

You can still use $A = \frac{1}{2} \times base \times height$ , but you need to find the perpendicular height - the shortest distance from the base to the opposite vertex.

Can I use any side as the base?

Yes! You can choose any side as the base, but then you must use the perpendicular distance to that side as the height. The area will always be the same.

What units should my answer have?

Area is always in square units. If your measurements are in centimeters, the area is in cm². If no units are given, just write the number like '21'.

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