i keep on getting stuck with this
Ok...a rhombus with 6 inch sides....two 120 degree angles....two altitudes are drawn from on of the 120 degree angles and they divide the rhombus in to 3 pieces...i need the area of the three pieces.......i got pretty close but im not sure if im right...
the other two angles are 60 degress
the two triangles the altitude makes are 30-60-90
the lengths of the two right triangles are 3, 6, 5.19615
the inner kite between the to right triangles are 3, 3, 5.19615, 5.19615
one diagonal of the kite is 5.19615
i have two different answers...one works when i check it, but it doesnt seem possible...the two diagonals are 5.9999 and 10.39 (this one works, but doesnt seem right) and the other one, one diagonal of the whole rhombus is 8.339
not sure if any of this helps but w.e
the rhombus consists of two congruent equilateral triangles.
One of the right triangles is the half of one equilateral triangle, that means the area of a right triangle is a quarter of the area of the complete rhombus.
The inner kite must have an area which is the half of the complete rhombus.
Therefore you only must know the area of the rhombus:
A_(rhombus) = 2 * A_(equilateral triangles)
A_(rhombus) = 2 * (1/2)* 6'' * (1/2) * 6'' * sqrt(3)
A_(rhombus) = 18 squinches * sqrt(3) ≈ 31.1769 square inches
A_(right triangle) = (1/4) * A_(rhombus) ≈ 7.7942
A_(inner kite) = (1/2) * A_(rhombus) ≈ 15.5885