Question

prove area of triangle=1\2 ×base ×height

Answer 1

Actually this proof was given to right angles triangles and because of this we follow it for every triangles, Here is the proof for right angled triangles,

We know that, In a Right angled Quadrilaterals such as Square of rectangle, if we observe 1 diagonal divides the quadrilateral into 2 equal parts,

Now let us take Rectangle as an example, Take a rectangle with sides, b and h, b for base, and h for height ( In general, Rectangle has, l and b),

Now take any of the diagonal, We can observe that, it divided rectangle into 2 equal parts, Which means, Area of Triangle = 1/2* Area of Rectangle,

Area of rectangle is multiplication of consecutive sides => Area = b*h,

Now, Area of Triangle = 1/2 * Base * Height, and this is why we follow it !

Hope you understand, Have a Great Day ! Merry Christmas !
Thanking you, Bunti 360 !

Answer 2

Consider a rectangle ABCD ,It is divided into two congruent parts and that parts are triangles.

In the Rectangle, Length of AB=CD = a

Length of BC = DA = b

Now Area of Rectangle ABCD = AREA OF ABD + AREA OF CBD

AS BOTH TRIANGLES ARE CONGRUENT, THEIR AREAS ARE EQUAL .

Now, Area of Rectangle ABCD = 2( Area of triangle ABD)

We know that Area of rectangle = lb = a×b = ab .

Now From the relationship,
Area of triangle = ab/2 = 1/2 * base * height.

Hence proved!