Calculate Triangle Area: 7-Unit Height and 4.5-Unit Base Problem

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

The base is the bottom side of the triangle (horizontal line BC = 4.5), and the height is the perpendicular distance from the opposite vertex to the base (vertical line AE = 7).

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

A triangle is exactly half of a rectangle with the same base and height. So we calculate the rectangle area (base × height) then divide by 2!

Q: What if I get the wrong answer by switching base and height?

If you use base = 7 and height = 4.5, you get $ \frac{1}{2} \times 7 \times 4.5 = 15.75 $. Same answer! This happens because multiplication is commutative (a × b = b × a).

Q: Do I need to include units in my final answer?

Yes! Since we're finding area, the answer should be in square units. Write 15.75 square units or 15.75 units².

Q: Can I use this formula for any triangle?

Absolutely! $ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} $ works for any triangle as long as you measure the height perpendicular to the chosen base.

Triangle Area with Given Height and Base

Calculate the area of the following triangle:

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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

00:02 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 relevant values and proceed to solve

00:27 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 following triangle:

Step-by-step solution

To find the area of the triangle, we will use the formula for the area of a triangle:

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

From the problem:

The length of the base $BC$ is given as 7 units.
The height from point $A$ perpendicular to the base $BC$ is given as 4.5 units.

Substitute the given values into the area formula:

$\text{Area} = \frac{1}{2} \times 7 \times 4.5$

Calculate the expression step-by-step:

$\text{Area} = \frac{1}{2} \times 31.5$

$\text{Area} = 15.75$

Therefore, the area of the triangle is $15.75$ square units. This corresponds to the given choice: $15.75$ .

Final Answer

15.75

Key Points to Remember

Essential concepts to master this topic

Formula: Area = 1/2 × base × height for any triangle
Technique: Multiply 1/2 × 4.5 × 7 = 15.75 square units
Check: Units are squared and calculation: 4.5 × 7 ÷ 2 = 15.75 ✓

Common Mistakes

Avoid these frequent errors

Confusing base and height measurements
Don't use base = 4.5 and height = 7 = Area of 17.5! The diagram clearly shows the horizontal base BC = 4.5 and vertical height AE = 7. Always identify which measurement is the base (horizontal) and which is the height (perpendicular distance).

Practice Quiz

Test your knowledge with interactive questions

Calculate the area of the right triangle below:

FAQ

Everything you need to know about this question

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

The base is the bottom side of the triangle (horizontal line BC = 4.5), and the height is the perpendicular distance from the opposite vertex to the base (vertical line AE = 7).

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

A triangle is exactly half of a rectangle with the same base and height. So we calculate the rectangle area (base × height) then divide by 2!

What if I get the wrong answer by switching base and height?

If you use base = 7 and height = 4.5, you get $\frac{1}{2} \times 7 \times 4.5 = 15.75$ . Same answer! This happens because multiplication is commutative (a × b = b × a).

Do I need to include units in my final answer?

Yes! Since we're finding area, the answer should be in square units. Write 15.75 square units or 15.75 units².

Can I use this formula for any triangle?

Absolutely! $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ works for any triangle as long as you measure the height perpendicular to the chosen base.

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