Area of an Oblique Triangle - SAS & SSS - Heron's Formula, Trigonometry

TL;DR

Learn how to find the area of a triangle when given all three sides using Heron's Formula.

Transcript

in this lesson we're going to focus on calculating the area of a triangle when we're given all three sides so let's say if this is 5 this is 6 and this is 7. let's call this a b and c so in this example side a is seven side b is six side c is five now we need to use something called heron's formula the first thing we need to do is calculate s s is ... Read More

Key Insights

• 🔺 Heron's Formula is used to find the area of a triangle when given all three side lengths.
• 🔺 The first step is to calculate the value of "s," which is half of the triangle's perimeter.
• ⌛ The area can then be found by using the square root of "s" times "s" minus each side length.
• 🔺 Heron's Formula works for any type of triangle, not just right triangles.
• ❎ The values inside the square root can be simplified if they are not perfect squares.
• 🔺 Oblique triangles can also have their area calculated using the formula 1/2 * side1 * side2 * sine of the included angle.
• 🔺 For a side angle side triangle, any combination of sides and angles can be used to calculate the area as long as all three letters are different.

Questions & Answers

Q: What is Heron's Formula used for?

Heron's Formula is used to calculate the area of a triangle when given all three side lengths.

Q: How do you find the value of "s" in Heron's Formula?

To find "s," you add up all three side lengths and divide the sum by 2.

Q: Can Heron's Formula be used for only right triangles?

No, Heron's Formula can be used for any type of triangle, including acute and obtuse triangles.

Q: How can you simplify the square root expression in Heron's Formula?

If the values inside the square root are not perfect squares, you can multiply them together and leave it as the square root of their product.

Summary & Key Takeaways

• It is possible to calculate the area of a triangle when given all three sides using Heron's Formula.

• Heron's Formula involves finding the value of "s," which is half of the triangle's perimeter.

• The area can then be calculated using the square root of "s" times "s" minus each side length.