Question

why area of triangle is 1/2 base×height

Answer 1

Taking any rectangle, choose a side to remain fixed, and translate its opposite side freely along a line parallel to the fixed side.

This process is called shearing. Shearing preserves area.

The original rectangle has an area of base⋅heightbase⋅height, and all of the parallelograms created by shearing have that same area.

Now cut the original rectangle in half along the diagonal to create a right triangle whose area is 12⋅base⋅height.

Answer 2

$\blue{\huge{\boxed{\star\: Solution \: \star}}}$

===> As we know

==>

$\red{ \small{area \: of \: parallelogram \: = \: base \: \times height}}$

==> When we make diagonal of that parallelogram it will make two triangle

So,

◆Area of parallelogram = 2 × area of two triangles

===> Area of triangle must be half of that parallelogram.

◆Hence area of triangle is 1/2 × b × h
$\green{ \boxed{ \underline{ \small{area \: of \: triangle \: = \frac{1}{2} \times b \times h}}}}$