Area of Triangle proof
A triangle is one of the basic shapes of geometry: a polygon with three corners or vertices and three sides or edges which are line segments. The area of the triangle is determine to the how many square units are there in the triangle. A triangle with vertices A, B, and C is denoted triangle ABC. (source: Wikipedia)
Proof of the area of a triangle:
We can prove the area of triangle formula by using the rectangle.
In the rectangle ABCD and let ‘h’ is the height and ‘b’ breath as shown below:
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The area of this rectangle is b × h
By draw the diagonal for that rectangle ,we get two right triangle.
The area is measured as the half region of the rectangle. For example, the area of triangle ABC is 1/2(b × h)
in the above diagram the triangle is in the form of incomplete and we cannot make it as right and these type of triangle is called special triangle
If we want to prove the formula then it should be same to the any arbitrary function such as scalene triangle, it will be work on the special triangles such as equilateral, isosceles or right triangle.
Let us start the scalene triangle ABC which has nothing special about it
Then, we draw the height from the vertex B and label it as you see below:
Area of triangle ABC = area of triangle ABE + area of triangle CBE
Area of triangle ABC = `(y*h)/(2)+ (x * h)/(2) `
Area of triangle ABC = `(y * h + x * h)/(2) `
Area of triangle ABC =`( h *(y + x))/(2) `
Notice that y + x is the length of the base of triangle ABC.
hus, y + x = b
Therefore, area of triangle ABC = `(h * b)/(2)`
Algebra is widely used in day to day activities watch out for my forthcoming posts on Area of an Equilateral Triangle Formula and solve my math problem for me I am sure they will be helpful.
Example area of triangle proof problems:
1) Prove that the area of a triangle is 42 m2 which has the base of 14 m and a height of 6 m.
Proof:
Area of a triangle = 1/2 b h
= 1/2 (14) (6)
= 42 m2
2) Find the area of a triangle with base of 16 m and a height of 5 m.
Solution:
Area of a triangle = 1/2 b h
= 1/2 (16) (5)
= 40 m2
3) Find the area of a triangle through base of 150 mm and a height of 60 mm.
Solution:
Area of a triangle = 1/2 b h
= 1/2(150) (60)
= 4500 mm2
Proof of the area of a triangle:
We can prove the area of triangle formula by using the rectangle.
In the rectangle ABCD and let ‘h’ is the height and ‘b’ breath as shown below:
Looking out for more help on Area of a Triangle Calculator in algebra by visiting listed websites.
The area of this rectangle is b × h
By draw the diagonal for that rectangle ,we get two right triangle.
The area is measured as the half region of the rectangle. For example, the area of triangle ABC is 1/2(b × h)
in the above diagram the triangle is in the form of incomplete and we cannot make it as right and these type of triangle is called special triangle
If we want to prove the formula then it should be same to the any arbitrary function such as scalene triangle, it will be work on the special triangles such as equilateral, isosceles or right triangle.
Let us start the scalene triangle ABC which has nothing special about it
Then, we draw the height from the vertex B and label it as you see below:
Area of triangle ABC = area of triangle ABE + area of triangle CBE
Area of triangle ABC = `(y*h)/(2)+ (x * h)/(2) `
Area of triangle ABC = `(y * h + x * h)/(2) `
Area of triangle ABC =`( h *(y + x))/(2) `
Notice that y + x is the length of the base of triangle ABC.
hus, y + x = b
Therefore, area of triangle ABC = `(h * b)/(2)`
Algebra is widely used in day to day activities watch out for my forthcoming posts on Area of an Equilateral Triangle Formula and solve my math problem for me I am sure they will be helpful.
Example area of triangle proof problems:
1) Prove that the area of a triangle is 42 m2 which has the base of 14 m and a height of 6 m.
Proof:
Area of a triangle = 1/2 b h
= 1/2 (14) (6)
= 42 m2
2) Find the area of a triangle with base of 16 m and a height of 5 m.
Solution:
Area of a triangle = 1/2 b h
= 1/2 (16) (5)
= 40 m2
3) Find the area of a triangle through base of 150 mm and a height of 60 mm.
Solution:
Area of a triangle = 1/2 b h
= 1/2(150) (60)
= 4500 mm2