The eighth grade mathematics exercise book answer 5.2( 1) the sixth question.

As can be seen from the figure, in the rhombic ABCD, e is the midpoint of BC, and AE⊥BC,BE=2.

The number of times to find (1)∠BCD.

(2) Diagonal length AC and BD

(3) the area of rhombic ABCD

(1) Because e is the midpoint of BC, BE=2.

So BC=4

Because quadrilateral ABCD diamond ABCD

So BC=AB=4.

Because AE⊥BC

So the triangle AEB is a right triangle.

Because BE= 1/2AB=2.

So ∠BAE=30 degrees

∠ABE=60 degrees

So ∠BCD= 120 degrees.

② Because AE⊥BC

So in the right triangle AEB,

(AE) Square = 4*4-2*2= 12

So AE=2√3

It can also be used as (AC) square = 12+2*2= 16.

So AC=4

So triangle ABC is an equilateral triangle.

So ∠BAC=60 degrees.

Because the quadrilateral ABCD is a diamond.

So ∠ABD= 1/2∠ABE=30 degrees.

Because AO= 1/2AB=2 in triangle ABO.

So the triangle ABO is a right triangle.

So BO=AE=2√3.

So BD=4√3

(3)S= 1/2*BD*AC

= 1/2*4*4√3

=8√3