Calculate Triangle Area: Find Area with Sides 5, 7, and 8.6

Q: How do I know which sides to use for the area formula?

In a right triangle, use the two sides that meet at the right angle (the legs). These are perpendicular to each other, so one serves as the base and the other as the height.

Q: Why can't I use the longest side (8.6) in my calculation?

The longest side is the hypotenuse, which is opposite the right angle. It's neither the base nor the height of the triangle, so using it gives an incorrect area calculation.

Q: What if I don't know which angle is the right angle?

Look for the square symbol in the corner, or remember that the right angle is opposite the longest side (hypotenuse). The two shorter sides form the right angle.

Q: Is there another way to find the area if I have all three sides?

Yes! You can use Heron's formula, but for right triangles, the simple formula $ \frac{leg_1 \times leg_2}{2} $ is much easier and faster.

Q: How can I check if my triangle is actually a right triangle?

Use the Pythagorean theorem: $ 5^2 + 7^2 = 25 + 49 = 74 $ and $ 8.6^2 = 73.96 $. Since these are approximately equal, it confirms we have a right triangle!

Right Triangle Area with Given Side Lengths

What is the area of the triangle in the drawing?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:11 Let's find the area of this triangle together.

00:15 We'll use the triangle area formula: base times height, divided by 2.

00:20 Now, let's plug in our numbers. We have a base of 7 and a height of 5, so that's 7 times 5, divided by 2.

00:29 Let's solve this step by step. First, multiply 7 times 5, which gives us 35. Then divide 35 by 2.

00:39 And there we have it! The area of our triangle is 17.5 square units. That wasn't too hard, was it?

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the area of the triangle in the drawing?

Step-by-step solution

First, we will identify the data points we need to be able to find the area of the triangle.

the formula for the area of the triangle: height*opposite side / 2

Since it is a right triangle, we know that the straight sides are actually also the heights between each other, that is, the side that measures 5 and the side that measures 7.

We multiply the legs and divide by 2

$\frac{5\times7}{2}=\frac{35}{2}=17.5$

Final Answer

17.5

Key Points to Remember

Essential concepts to master this topic

Rule: For right triangles, area equals half the product of perpendicular sides
Technique: Identify the legs: Area = $\frac{5 \times 7}{2} = 17.5$
Check: Two perpendicular sides form the base and height for calculation ✓

Common Mistakes

Avoid these frequent errors

Using the hypotenuse in area calculations
Don't use the hypotenuse (8.6) in the area formula = wrong answer of 21.5 or 30.1! The hypotenuse is neither the base nor height of a right triangle. Always identify the two perpendicular sides (legs) and use them as base and height.

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 sides to use for the area formula?

In a right triangle, use the two sides that meet at the right angle (the legs). These are perpendicular to each other, so one serves as the base and the other as the height.

Why can't I use the longest side (8.6) in my calculation?

The longest side is the hypotenuse, which is opposite the right angle. It's neither the base nor the height of the triangle, so using it gives an incorrect area calculation.

What if I don't know which angle is the right angle?

Look for the square symbol in the corner, or remember that the right angle is opposite the longest side (hypotenuse). The two shorter sides form the right angle.

Is there another way to find the area if I have all three sides?

Yes! You can use Heron's formula, but for right triangles, the simple formula $\frac{leg_1 \times leg_2}{2}$ is much easier and faster.

How can I check if my triangle is actually a right triangle?

Use the Pythagorean theorem: $5^2 + 7^2 = 25 + 49 = 74$ and $8.6^2 = 73.96$ . Since these are approximately equal, it confirms we have a right triangle!

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