Question

Give me a rhombus ABCD with BC =25 and BD= 30 find AC and the area of ABCD

Answer 1

300 u²

1) Let's start by sketching out this:

2) Since a Rhombus have 4 congruent sides, then we can state that 4 sides are 25 units, and we need to find out the other Diagonal (AC)

Applying the Pythagorean Theorem, to Triangle COD

a² =b² +c²

25² = 15² +c²

625 = 225 + c² subtract 225 from both sides

625-225 = c²

400 = c²

√c² =√400

c =20

2.2) Now, we can calculate the area, applying the formula for the area of a rhombus (the product of its diagonals).

`\begin{gathered} A=(D\cdot d)/(2) \\ A=(40\cdot30)/(2) \\ A=(1200)/(2) \\ A\text{ = 600} \end{gathered}`

3) Hence, the answer is 300 u²