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

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 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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