Find s, the length of segment AE .

Question

The area of rhombus ABCD is 350 cm2 and  28 cm. Find , the length of segment . Approximate to the nearest tenth, if necessary.

               cm

Answer 1

Assuming that point E is the point of intersection of the two diagonals of the rhombus, we will begin with the area formula for a rhombus which is A = 1/2( d₁ x d₂ ), where d₁ and d₂ are the two diagonals of the rhombus. Since we are already given the area and the length of one diagonal, we insert those values into the formula:

350 = 1/2 (28)( AC). Solving for AC, we find that AC = 25. Since the two diagonals in any rhombus bisect each other, we divide AC by 2 to find that AE = 12.5, so x = 12.5 cm.