They have congruent heights that are drawn perpendicular towards the base. By the same token, △ ABD and △ CBD are congruent triangles, which means they have congruent heights. Therefore, the diagonals are perpendicular bisectors.
c Let's add the given information to the diagram.
From Part A we know that the diagonals are perpendicular bisectors. This must mean that the diagonals bisect the angles of the rhombus. The diagonals create four congruent triangles according to the SAS (Side-Angle-Side) Congruence Theorem.
If we can find the area of one triangle we can determine the area of the rhombus by multiplying this by 4. Notice that these triangles are 30^(∘)-60^(∘)-90^(∘) triangles, which means the shorter leg is half the length of the hypotenuse and the longer leg is sqrt(3) times longer than the shorter leg.
Now we can calculate the area of one of the triangles. If we multiply this by 4 we get the area of the rhombus.
Area: (1/2* 4* 4sqrt(3))4≈ 55.42 units^2
