Calculate Triangle Area: Using Height 5 and Base 4 Units

Triangle Area with Base and Height

Calculate the area of the following triangle:

444555AAABBBCCCEEE

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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
00:06 (base(BC) x height(AE)) divided by 2
00:10 Substitute in the appropriate values and proceed to solve
00:20 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Calculate the area of the following triangle:

444555AAABBBCCCEEE

2

Step-by-step solution

The formula for calculating the area of a triangle is:

(the side * the height from the side down to the base) /2

That is:

BC×AE2 \frac{BC\times AE}{2}

We insert the existing data as shown below:

4×52=202=10 \frac{4\times5}{2}=\frac{20}{2}=10

3

Final Answer

10

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area of triangle equals base times height divided by 2
  • Technique: Multiply base 4 × height 5, then divide by 2: 20÷2=10
  • Check: Verify units are square units and result is positive ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to divide by 2
    Don't just multiply base × height = 4 × 5 = 20! This gives you the area of a rectangle, not a triangle. Always divide by 2 because a triangle is exactly half of a rectangle with the same base and height.

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?

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A triangle is exactly half of a rectangle! If you draw a rectangle with the same base and height, then draw a diagonal, you get two identical triangles. So triangle area = rectangle area ÷ 2.

How do I identify which side is the base and which is the height?

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The height is always the perpendicular distance from one vertex to the opposite side (the base). In this diagram, the vertical line AE with length 5 is perpendicular to the horizontal base BC with length 4.

What if I use the wrong base and height?

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As long as your height is perpendicular to your chosen base, you'll get the correct area! A triangle has three possible base-height pairs, and they all give the same area.

Can the area ever be negative?

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Never! Area represents space covered, which is always positive. If you get a negative result, check your calculation - you likely made an error.

What units should my answer have?

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Area is always in square units! If your base and height are in centimeters, your area is in square centimeters (cm²). Here, since no units are given, we just say 10 square units.

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