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Lesson 2: Area of parallelograms and triangles

# Area of a triangle

Understand why the formula for the area of a triangle is one half base times height, which is half of the area of a parallelogram.

## Want to join the conversation?

• is there another formula
• Interesting question!

Given the length of any base and the height (altitude) perpendicular to the side that is chosen as the base, the area formula of one half base times height is about as simple as it gets.

If instead the lengths of the three sides are given (but no heights are given), there is a much more complex formula for the area of the triangle, called Heron's formula. Let a, b, and c represent the lengths of the sides, and let S = (a+b+c)/2, that is, S represents half the perimeter.
Then the area is given by A = squareroot[S(S - a)(S - b)(S - c)].
• Why is math important?
• Math helps us think analytically and have better reasoning abilities. Analytical thinking refers to the ability to think critically about the world around us. ... Analytical and reasoning skills are essential because they help us solve problems and look for solutions
• Is the answer still units squared or square units?
• Yes, the answer will be in units squared (even though you are measuring a △ and not a □)!
• What if the tringle has 1 number and you have to find the area?
• To calculate the area of a triangle given one side and two angles, solve for another side using the Law of Sines, then find the area with the formula: area = 1/2 × b × c × sin(A) video link is https://youtu.be/wTkH288r84s.
Ty
• i really don't get this concept can any one discripe it in a better form or discription
• So if you know how to find area of a rectangle or square this should make sense. Use the formula Base x Height divided by 2. Hope that helped!
• I still don't get it I am bad at math can someone explain this to me?
• Ok, so let's get started with right triangles.
Visualise a right triangle as a half of a rectangle. The hypotenuse is the diagonal of the rectangle. The hypotenuse is the longest side of a triangle. The legs of the triangles are the 2 adjacent sides of the rectangle. Adjacent sides are sides that share a common point. In other words, adjacent sides are side-by-side. The area of a rectangle is length times the breadth, or lb. Now we know our right triangle is half of our rectangle. So the area will be half of that of the rectangle. Therefore, the area is lb/2.
Watch this video where Sal describes the proof of Triangles.
• how do you find the base if you know the area and the height?
• we know that Area = (base * height)/2 (formula for area of a triangle). if we know the area, suppose it is 4 for this example, and the height is 2 we get
4=(x*2)/2.
multiply by 2 on both sides to get
8=x*2, divide both sides by 2 to get
4=x, or 4=the base
use this method for the actual numbers
• why is learning important
• Learning is important so that you know what to do. If you hadn't learned how to type or communicate in English, you would not have been able to type that question. Learning is also important, because you usually will not be accepted into college with low grades. College is important because a lot of jobs will accept you if you have gone through college. If you are stuck with a job that you do not like or does not pay you enough, it is very difficult to get out of it.
• Given the length of any base and the height (altitude) perpendicular to the side that is chosen as the base, the area formula of one half base times height is about as simple as it gets.

If instead the lengths of the three sides are given (but no heights are given), there is a much more complex formula for the area of the triangle, called Heron's formula. Let a, b, and c represent the lengths of the sides, and let S = (a+b+c)/2, that is, S represents half the perimeter.
Then the area is given by A = squareroot[S(S - a)(S - b)(S - c)].
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