Why is the area of a triangle 1 2bh
Formula for Area of a Triangle - Why?
let's talk about the formula for finding
the area of a triangle area equals
one-half base times height we could just
plug the numbers into the formula and
get an answer but what does it mean
where does that 1/2 come from
we'll get to that but first let's get
rid of that half wait a minute that
looks like the formula for finding the
area of a rectangle area equals length
times width and that tells us how many
square units are inside the rectangle
rectangles are a cinch because of all
those right angles interestingly area
for parallelograms that don't have right
angles like these are solved in a
similar fashion we just focus on base
and height instead of length and width
but watch this area equals base times
height if you cut off this piece and
move it over here you can see we have a
rectangle with the length of 6 and a
height of 4 the areas of both the
rectangle and this parallelogram are the
same okay moving on why am I talking
about different types of parallelograms
this is supposed to be about triangles
all right here we go
area of a triangle equals one-half base
times height take this right triangle
here with a base of 10 inches and a
height of 8 inches we want to know the
area or how many square inches the space
inside can hold so I'm going to take
another triangle same size and shape or
congruent to this one just in a
different color to help you see now if I
line these up with their hypotenuse is
completely touching you see I now have a
rectangle with a length of 10 inches and
a width of 8 inches so you see it takes
two of the triangles here to make this
rectangle therefore the area of this
right triangle is going to be 1/2 the
area of this rectangle there it is the
1/2 from the formula of area of a
triangle area equals 1/2 base times
height as further proof if half across
this diagonal is difficult for you to
see look at it like this if I decompose
this triangle like this you'll see that
the triangle can fit into half of the
rectangle in this way to 1/2 of the base
times height not all triangles have
right angles though don't worry we'll
talk about those too let's copy and
rotate this
triangle just like we did before but
this time instead of getting a rectangle
we get a parallelogram you know that the
area of a parallelogram is base times
height and half of a parallelogram is a
triangle so no matter what angles are in
the triangle the area must be one-half
base times height
