Calculate Triangle Area: Right Triangle with Base 7 and Height 5

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

A triangle is exactly half of a rectangle! If you draw a rectangle with the same base and height, the triangle takes up exactly half the space inside it.

Q: What if my triangle doesn't look like a right triangle?

The triangle area formula $ \frac{1}{2} \times \text{base} \times \text{height} $ works for any triangle! The height is always the perpendicular distance from the base to the opposite vertex.

Q: What does the 8.6 measurement in the diagram represent?

The 8.6 is the hypotenuse (longest side) of this right triangle. We don't need it to find the area - we only need the base (7) and height (5) that form the right angle.

Triangle Area with Basic Formula Application

Calculate the area of the triangle below, if possible.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 If possible, calculate the triangle's area

00:03 Apply the formula for calculating the triangle's 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 below, if possible.

Step-by-step solution

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

Step 1: Identify the given base and height of the triangle.
Step 2: Apply the formula for the area of a triangle.
Step 3: Perform the necessary calculations to find the area.

Now, let's work through each step:
Step 1: The base of the triangle is given as 7 units, and the height is given as 5 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 our values, we have:
$\text{Area} = \frac{1}{2} \times 7 \times 5 = \frac{1}{2} \times 35 = 17.5$ .

Therefore, the area of the triangle is $17.5$ square units.

Final Answer

17.5

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals half times base times height
Technique: Substitute values: $\frac{1}{2} \times 7 \times 5 = 17.5$
Check: Verify units are squared and answer is reasonable for given dimensions ✓

Common Mistakes

Avoid these frequent errors

Forgetting to multiply by one-half
Don't just multiply base times height (7 × 5 = 35) = wrong answer! This gives the area of a rectangle, not a triangle. Always multiply by $\frac{1}{2}$ first in the triangle area formula.

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 multiply by 1/2 in the triangle area formula?

A triangle is exactly half of a rectangle! If you draw a rectangle with the same base and height, the triangle takes up exactly half the space inside it.

Does it matter which side I call the base?

Not at all! You can use any side as the base, but the height must be perpendicular (at a 90° angle) to whichever side you choose as the base.

What if my triangle doesn't look like a right triangle?

The triangle area formula $\frac{1}{2} \times \text{base} \times \text{height}$ works for any triangle! The height is always the perpendicular distance from the base to the opposite vertex.

How can I tell if 17.5 square units is a reasonable answer?

Check if it's between 0 and the rectangle area. Since base × height = 7 × 5 = 35, your triangle area should be less than 35. At 17.5, that's exactly half - perfect!

What does the 8.6 measurement in the diagram represent?

The 8.6 is the hypotenuse (longest side) of this right triangle. We don't need it to find the area - we only need the base (7) and height (5) that form the right angle.

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