I love these. It's often called the Shoelace Formula. It actually works for the area of any 2D polygon.
We can derive it by first imagining our triangle in the first quadrant, one vertex at the origin, one at (a,b), one at (c,d), with (0,0),(a,b),(c,d) in counterclockwise order.
Our triangle is inscribed in the 
rectangle. There are three right triangles in that rectangle that aren't part of our triangle. When we subtract the area of the right triangles from the area of the rectangle we're left with the area S of our triangle.
That's the cross product in the purest form. When we're away from the origin, a arbitrary triangle with vertices 
will have the same area as one whose vertex C is translated to the origin.
We set 
That's a perfectly useful formula right there. But it's usually multiplied out:
That's the usual form, the sum of cross products. Let's line up our numbers to make it easier.
(1, 2), (3, 4), (−7, 7)
(−7, 7),(1, 2), (3, 4),
[tex]A = \frac 1 2 ( 1(7)-2(-7) + 3(2)-4(1) + -7(4) - (7)(3)
Answer:
GH = 17 units
GI = 39 units
HI = 39 units
Step-by-step explanation:
We are given the following information in the question:
Triangle GHI is an isosceles triangle.
The measures of side are:
It is given that
GI = HI
Thus, the measures of three sides are:
Answer:
the answer you are looking for is-10
Step-by-step explanation:
Answer: the answer is 5
Step-by-step explanation:
good luck
For this case we must indicate the cosine of A, of the figure shown. By definition:
Substituting the values we have:
So, we have to:
Answer:
Option D
