Calculate Triangle Area: Right Triangle with Height 4 and Base 7

Triangle Area with Given Height and Base

Calculate the area of the triangle below, if possible.

666777444

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's find the area of the triangle!
00:09 We use the formula for a triangle's area.
00:12 It's base times height, divided by two.
00:17 Now, plug in the given numbers and calculate.
00:21 And there you have it, our area solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Calculate the area of the triangle below, if possible.

666777444

2

Step-by-step solution

To solve this problem, we will follow these steps:

  • Step 1: Identify the relevant sides based on problem context
  • Step 2: Apply the standard triangle area formula
  • Step 3: Calculate the area based on the known values for base and height

Let's work through each step in detail:

Step 1: We are seeking to calculate the area of the triangle. We identified that the line segment of 4 units represents the height, and the base is 7 units.

Step 2: We will apply the formula for the area of a right triangle: Area=12×base×height \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} .

Step 3: Plug the values we have: Area=12×7×4=12×28=14 \text{Area} = \frac{1}{2} \times 7 \times 4 = \frac{1}{2} \times 28 = 14 .

Thus, the area of the triangle is 14 14 square units.

3

Final Answer

14

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area equals one-half times base times height
  • Technique: Area = 12×7×4=14 \frac{1}{2} \times 7 \times 4 = 14 square units
  • Check: Verify dimensions match diagram and right angle is present ✓

Common Mistakes

Avoid these frequent errors
  • Confusing base and height identification
    Don't guess which side is the base or height without checking the right angle! This leads to using wrong dimensions like 6×4=24 instead of 7×4=28. Always identify the perpendicular sides: the horizontal base (7) and vertical height (4).

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 side is the base and which is the height?

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In a right triangle, the base is horizontal and the height is vertical. Look for the right angle symbol (small square). The two sides forming the right angle are your base and height - not the hypotenuse!

Why do we multiply by 1/2 in the triangle area formula?

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A triangle is exactly half of a rectangle! If you drew a rectangle with the same base and height, the triangle would fill exactly half of it. That's why we use 12 \frac{1}{2} .

What if I accidentally used the side labeled 6 in my calculation?

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The side labeled 6 is the hypotenuse (longest side). For area calculations, we only use the two sides that form the right angle. Check your diagram again for the perpendicular sides!

Do I need to include units in my final answer?

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Yes! Since we're calculating area, your answer should include square units. For example: 14 square units, 14 units², or 14 cm² if specific units were given.

Can I use this formula for any triangle?

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This specific formula works for any triangle as long as you have a true base and its corresponding perpendicular height. The height must form a 90° angle with the base.

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