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

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

A triangle is exactly half of a rectangle! If you draw a rectangle with the same base and height as your triangle, the triangle covers exactly half the space. That's why we multiply base × height, then divide by 2.

Q: How do I identify the base and height in a right triangle?

In a right triangle, the base and height are the two perpendicular sides that form the right angle. The longest side (hypotenuse) is never used in the area formula - only the two shorter sides that meet at 90°.

Q: Can I use the hypotenuse length (8.06) to find the area?

No! The area formula only uses base and height (the perpendicular sides). The hypotenuse length can help verify your triangle is correct, but it's not needed for area calculations.

Q: What units should my answer have?

Since area measures square space, your answer should be in square units. If the sides are in centimeters, the area is in square centimeters (cm²). Always include 'square' in your units!

Triangle Area with Base-Height Formula

Calculate the area of the triangle using the data in the figure below.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the triangle's area

00:03 Apply the formula for calculating triangle area

00:06 (base x height) divided by 2

00:09 Substitute in the relevant values according to the given data and proceed to solve for the area

00:12 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 triangle using the data in the figure below.

Step-by-step solution

To solve for the area of a triangle when the base and height are given, we'll use the formula:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

Given:

Base = $4$ units
Height = $7$ units

Apply the formula:

$\begin{aligned} \text{Area} &= \frac{1}{2} \times 4 \times 7 \\ &= \frac{1}{2} \times 28 \\ &= 14 \end{aligned}$

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

Final Answer

Key Points to Remember

Essential concepts to master this topic

Area Formula: Area = $\frac{1}{2} \times \text{base} \times \text{height}$
Technique: Multiply base (4) and height (7), then divide by 2
Check: Verify calculation: $\frac{1}{2} \times 4 \times 7 = 14$ square units ✓

Common Mistakes

Avoid these frequent errors

Forgetting to divide by 2
Don't calculate just base × height = 4 × 7 = 28! This gives double the actual area because the formula requires dividing by 2. Always remember that triangle area is half the area of a rectangle with the same base and height.

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 we divide by 2 in the triangle area formula?

A triangle is exactly half of a rectangle! If you draw a rectangle with the same base and height as your triangle, the triangle covers exactly half the space. That's why we multiply base × height, then divide by 2.

How do I identify the base and height in a right triangle?

In a right triangle, the base and height are the two perpendicular sides that form the right angle. The longest side (hypotenuse) is never used in the area formula - only the two shorter sides that meet at 90°.

What if the triangle isn't drawn with the base horizontal?

It doesn't matter how the triangle is oriented! You can choose any side as the base, and the height will be the perpendicular distance from that base to the opposite vertex.

Can I use the hypotenuse length (8.06) to find the area?

No! The area formula only uses base and height (the perpendicular sides). The hypotenuse length can help verify your triangle is correct, but it's not needed for area calculations.

What units should my answer have?

Since area measures square space, your answer should be in square units. If the sides are in centimeters, the area is in square centimeters (cm²). Always include 'square' in your units!

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