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Course: Algebra basics>Unit 1

Lesson 9: Area of triangles

Area of a triangle

The area of a rectangle and a parallelogram is found by multiplying the base by the height. For a triangle, the area is half of a parallelogram's, so it's calculated by multiplying the base by the height and then dividing by 2.

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• 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
• 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
• 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 □)!
• 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.
• This is so much better than other videos and teacheRs explaining
• This video has broken down my brain. I was studying in school for 10 years and hadn`t understood why is it 1/2bh, but this video... oh my god
• if you don't understand it just do the following to find the area of a triangle:

Base x Height ÷ 2 = Area
Example:
5(b) x 4(h) = 20
20 ÷ 2 = 10
Area = 10
(1 vote)
• 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