Calculate Triangle Area: Right Triangle with Height 5.5 and Base 7.8

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

A triangle is half of a rectangle! If you imagine completing the rectangle, it would have area = base × height. Since a triangle is exactly half that rectangle, we divide by 2.

Q: Does it matter which side I call the base and which is the height?

No, it doesn't matter! You can use either perpendicular side as base or height. The formula $ \frac{1}{2} \times \text{base} \times \text{height} $ works the same way.

Q: What if the triangle isn't a right triangle?

For non-right triangles, you need to find the perpendicular height from one vertex to the opposite side (base). The formula stays the same, but finding the height is trickier.

Q: How can I double-check my triangle area calculation?

Multiply your answer by 2 - you should get base × height. In this problem: 21.45 × 2 = 42.9, which equals 7.8 × 5.5 ✓

Q: What units should my answer have?

Area is always measured in square units. If your measurements are in centimeters, the area is in cm². If no units are given, write "square units".

Triangle Area with Right Angle Properties

Calculate the area of the triangle, if possible.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:13 Let's find the area of the triangle.

00:16 We will use the formula to find the area.

00:20 It's base times height, divided by 2.

00:24 Now, let's put in the numbers and solve it.

00:29 And there you have 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, if possible.

Step-by-step solution

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

Step 1: Identify the given information:

The base of the triangle is $7.8$ units.
The height of the triangle is $5.5$ units.

Step 2: Apply the formula for the area of a right triangle:

The formula for the area of a triangle is:

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

Step 3: Perform the necessary calculations:

Substitute the values we have:

\text{Area} = \frac{1}{2} \times 7.8 \times 5.5

Calculating further:

\text{Area} = \frac{1}{2} \times 42.9

\text{Area} = 21.45

Therefore, the area of the triangle is $21.45$ square units.

This matches with choice 4 provided: 21.45.

Final Answer

21.45

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals half times base times height
Calculation: Area = ½ × 7.8 × 5.5 = 21.45
Check: Multiply result by 2 to get base × height: 21.45 × 2 = 42.9 ✓

Common Mistakes

Avoid these frequent errors

Using base times height without dividing by 2
Don't calculate 7.8 × 5.5 = 42.9 as the final answer! This gives you twice the actual area because you forgot the ½ factor. Always remember the area formula includes dividing by 2 or multiplying by ½.

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 half of a rectangle! If you imagine completing the rectangle, it would have area = base × height. Since a triangle is exactly half that rectangle, we divide by 2.

Does it matter which side I call the base and which is the height?

No, it doesn't matter! You can use either perpendicular side as base or height. The formula $\frac{1}{2} \times \text{base} \times \text{height}$ works the same way.

What if the triangle isn't a right triangle?

For non-right triangles, you need to find the perpendicular height from one vertex to the opposite side (base). The formula stays the same, but finding the height is trickier.

How can I double-check my triangle area calculation?

Multiply your answer by 2 - you should get base × height. In this problem: 21.45 × 2 = 42.9, which equals 7.8 × 5.5 ✓

What units should my answer have?

Area is always measured in square units. If your measurements are in centimeters, the area is in cm². If no units are given, write "square units".

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