Triangle Area Formula: Finding Height X When Area = 16 and Base = 4

Q: Why is the triangle area formula different from a rectangle?

A triangle is exactly half of a rectangle with the same base and height! That's why we multiply by $ \frac{1}{2} $ - we're finding half the rectangular area.

Q: How do I know which side is the base and which is the height?

The height must be perpendicular (at a 90° angle) to the base. In this diagram, you can see the dashed line showing x is perpendicular to the base of length 4.

Q: What if I get the formula backwards?

If you solve $ 16 = \frac{1}{2} \times x \times 4 $ instead of $ 16 = \frac{1}{2} \times 4 \times x $, you'll still get the same answer! Multiplication is commutative, so order doesn't matter.

Q: Can I use this formula for any triangle?

Yes! This formula works for any triangle as long as you know the base and the height perpendicular to that base. The shape doesn't have to be a right triangle.

Q: What if my answer doesn't work when I check it?

Double-check your arithmetic! Make sure you're using $ \frac{1}{2} $ in your formula and that you correctly isolated the variable. Recalculate step by step to find where the error occurred.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine the height X

00:03 Apply the formula for calculating the area of a triangle

00:08 (base(BC) x height(AE)) divided by 2

00:13 Substitute in the relevant values and calculate to determine the height X

00:26 Divide 4 by 2 to obtain 2

00:29 Isolate X

00:33 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

The area of the triangle is 16.

Calculate X.

2

Step-by-step solution

To solve this problem, we need to find the value of $x$ , given that the area of the triangle is 16 and the base is known to be 4.

Step 1: Identify known values.
We know the area $A = 16$ and base $b = 4$ .
Step 2: Apply the triangle area formula:
$A = \frac{1}{2} \times b \times h$ , where $h$ is the height we need to calculate.
Step 3: Solve for height $x$ .
Substitute values into the formula: $16 = \frac{1}{2} \times 4 \times x$ .
Step 4: Perform the necessary calculations:
Simplify the equation: $16 = 2 \times x$ .
Divide both sides by 2 to solve for $x$ .

The calculation simplifies to $x = 8$ .

Therefore, the solution to the problem is $x = 8$ .

3

Final Answer

8

Key Points to Remember

Essential concepts to master this topic

Formula: Area = $\frac{1}{2} \times \text{base} \times \text{height}$
Technique: Rearrange to solve for height: $h = \frac{2 \times \text{Area}}{\text{base}}$
Check: Verify $\frac{1}{2} \times 4 \times 8 = 16$ matches given area ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by one-half in area formula
Don't use Area = base × height = 4 × 8 = 32! This ignores the crucial $\frac{1}{2}$ factor in the triangle area formula and gives double the actual area. Always remember triangle area is $\frac{1}{2} \times \text{base} \times \text{height}$ .

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why is the triangle area formula different from a rectangle?

+

A triangle is exactly half of a rectangle with the same base and height! That's why we multiply by $\frac{1}{2}$ - we're finding half the rectangular area.

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

+

The height must be perpendicular (at a 90° angle) to the base. In this diagram, you can see the dashed line showing x is perpendicular to the base of length 4.

What if I get the formula backwards?

+

If you solve $16 = \frac{1}{2} \times x \times 4$ instead of $16 = \frac{1}{2} \times 4 \times x$ , you'll still get the same answer! Multiplication is commutative, so order doesn't matter.

Can I use this formula for any triangle?

+

Yes! This formula works for any triangle as long as you know the base and the height perpendicular to that base. The shape doesn't have to be a right triangle.

What if my answer doesn't work when I check it?

+

Double-check your arithmetic! Make sure you're using $\frac{1}{2}$ in your formula and that you correctly isolated the variable. Recalculate step by step to find where the error occurred.

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Triangle Area Formula: Finding Height X When Area = 16 and Base = 4

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