Recall that the LL theorem, as well as the LA theorem, both apply only to right-triangles.
now, in the LL, if a right-triangle has congruent Legs with another, both right-triangles are congruent.
in the LA, if a right-triangle has one Leg and one Angle congruent with another right-triangle, then they're congruent.
well, in the LA, once you have a Leg and then an Angle touching that Leg, the angle is also touching another Leg, since it is an angle and is cornered by two Legs. The second Leg touched or stemming from that Angle, can only be of one possible length, because the first Leg and the Angle will constrain it to be of certain length.
and that is true for both triangles, and since both triangles will have a second Leg constrained to be a certain length, because of LA, then a second Leg will also be congruent on both right-triangles, so the theorem kinda becomes LAL theorem, Leg Angle Leg, but we can just do away with the Angle part and call it LL.
Answer: The area of the hexagonal base is 96 square roots of 3.
The hexagon is divided into 6 congruent triangles. All we have to do is find the area of one of these shapes and multiply by 6.
The base of each triangle is 8 because the triangles are equilateral and one side is already given. The height is 4 square roots of 3 because it is a 30/6090 triangle.
To find the area, we multiply 8 x 4 square roots of 3 and divide by 2 to get 16 square roots of 3.
Multiply 16 by 6 and you get 96 square roots of 3.
