Thread: What is the relationship between area of a rectangle and right triangle?

A triangle with the legs of lengths a and b has the area of a rectangle with its dimensions a and b.

The area of a triangle is:

A = 1/2 B*H
where A = area, B = base, and H = height:
The area of a rectangle is:
A= L * W
where: A = area, L = length, W= width

If you draw a rectangle then draw a line diagonal across it you will have two right triangles:

That shows and proves the formula of
A= 1/2 B*H for a triangle: because for any given height and base of a right triangle the area will be one half of the area of a rectangle with the same length and width as the height and base of a right triangle

area of rectangle = 2*area of right triangle

a*b = 2(1/2*a*b)

1/2 a b = area of triangle
a b = area of rectangle

it is half of a × b. HALF of a rectangle with the same lengths on either side of the 90 degrees.

A rectangle has length a and width b. The area will be a × b.

Now, suppose you have a right angle triangle with one of the side a and another side b. As this is a triangle with a right angle, a and b is lies on the same place as the a and b in the rectangle. And the area will be halved as the triangle will have a third line which goes from the end of line a to the end of line b.