Welcome to two examples of determining the area
of a triangle on grid.
And we're told each small square on the grid
has a side length of one meter.
Before we determine the area, we need to determine
the length of the base and the height.
Because we are using the grid to determine lengths,
we will let this side be the base.
Notice how the base has a length
of one, two, three, four, five meters.
We will label this b equals five meters.
The reason we are not using, let's say, this side
as the base is because we could not
easily determine this length using the grids.
And now the height is going to be the vertical distance
from the base to this high point here,
but because we have an obtuse triangle, we will need
to extend the base to the left as a dashed segment.
And now the length or distance from this high point
to the extension of the base will be the height.
Notice how the height is one, two,
three, four, five, six meters.
We will label this h equals six meters.
Recording the information below,
the length of the base is five meters, and the height
of the triangle is six meters.
The area of the triangle is the number of square meters
that will fit inside the triangle.
The area of a triangle is equal
to one half base times height,
or base times height divided by two,
which means for this triangle, the area is equal
to one half times five meters times six meters.
Before determining this product, though,
let's use the commutative property of multiplication
and change the order of this product.
Because one half times five is a mixed number,
or a decimal, let's change this to one half
times six times five, because one half times six
is equal to three.
This simplifies to three times five, which equals fifteen.
The area is fifteen square meters.
Which means exactly fifteen square meters will fit
inside the triangle.
Let's look at one more example.
Same question, different triangle.
Because we are using the grid to determine the lengths,
though, we will now let this side
of the triangle be the base.
Notice how the base has a length of one, two, three,
four, five, six, seven meters.
We will label this side b equals seven meters.
Again, the reason we're not selecting, let's say,
this side for the base, is because we cannot easily
determine the length using the grids.
And now if this is the base, the height is going to be
the vertical distance from the base to this point here
on the right, which should be this length here.
Notice how the height is one, two, three, four, five
six, seven, eight, nine, ten meters.
And according to the information below, the length
of the base is seven meters, the height of the triangle
is ten meters, and the area of the triangle
is equal to one half base times height.
In this case we have the area
equals one half times seven meters times ten meters.
Now, for this example, let's leave this product
in this order.
One half times seven, or one half times seven over one,
is equal to seven halves.
We have seven halves times ten.
Let's write ten as a fraction, with a denominator of one.
If we're multiplying, notice two and ten
share a common factor of two, there's one, two, and two,
and five twos in ten.
This simplifies to seven times five, which equals 35.
The area of the triangle equals 35 square meters,
which means exactly 35 square meters'll fit
inside the triangle.
I hope you found this helpful.