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

Q: Why do I multiply by ½ instead of just base × height?

A triangle is exactly half of a rectangle! If you draw a rectangle with base 7 and height 4, its area is 28. A triangle with the same base and height takes up only half that space, so 28 ÷ 2 = 14.

Q: Does it matter which side I call the base?

No! You can use any side as the base, as long as you use the perpendicular height to that base. The area will always be the same.

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

The formula $ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} $ works for all triangles! Just make sure the height is perpendicular (forms a 90° angle) to the base.

Q: How do I know if I have the right base and height?

Look for the right angle symbol (small square) in the diagram! This shows where the height meets the base at exactly 90°. In this problem, the base is 7 and height is 4.

Q: Can I write my answer as just 14 or do I need units?

Always include square units for area! Since the measurements don't specify units, write your answer as "14 square units" to show you're measuring area, not length.

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 triangle area

00:05 (base x height) divided by 2

00:07 Substitute in the relevant values according to the given data and solve to find the area

00:10 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 triangle, if possible.

2

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the base and height of the triangle.
Step 2: Substitute these values into the formula for the area of a triangle.
Step 3: Perform the calculation to determine the area.

Let's work through each step:

Step 1: From the given information, the base of the triangle is 7 units, and the height is 4 units.

Step 2: We'll use the formula for the area of a triangle:
$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

Step 3: Plugging in the values for the base and height, we have:
$\text{Area} = \frac{1}{2} \times 7 \times 4$

Performing the multiplication, we get:
$\text{Area} = \frac{1}{2} \times 28 = 14$

Therefore, the area of the triangle is $\textbf{14}$ square units.

3

Final Answer

14

Key Points to Remember

Essential concepts to master this topic

Formula: Area = ½ × base × height for any triangle
Calculation: Area = ½ × 7 × 4 = 14 square units
Check: Multiply result by 2: 14 × 2 = 28 = base × height ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by one-half
Don't just multiply base × height = 7 × 4 = 28! This gives the area of a rectangle, not a triangle. A triangle is exactly half the area of a rectangle with the same base and height. Always multiply by ½ or divide by 2.

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 do I multiply by ½ instead of just base × height?

+

A triangle is exactly half of a rectangle! If you draw a rectangle with base 7 and height 4, its area is 28. A triangle with the same base and height takes up only half that space, so 28 ÷ 2 = 14.

Does it matter which side I call the base?

+

No! You can use any side as the base, as long as you use the perpendicular height to that base. The area will always be the same.

What if the triangle isn't a right triangle?

+

The formula $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ works for all triangles! Just make sure the height is perpendicular (forms a 90° angle) to the base.

How do I know if I have the right base and height?

+

Look for the right angle symbol (small square) in the diagram! This shows where the height meets the base at exactly 90°. In this problem, the base is 7 and height is 4.

Can I write my answer as just 14 or do I need units?

+

Always include square units for area! Since the measurements don't specify units, write your answer as "14 square units" to show you're measuring area, not length.

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

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