Answer:
y = 40.5 cm
Step-by-step explanation:
The total area of the shape is 792 cm²
let's find the area of the four parallelograms
To do that we should calculate the area of the rhombus inside and then substract it from the total area
The area of a rhombus is given by the formula:
- A = [tex]\frac{d*d'}{2}[/tex] where d and d' are the diameters
Let A be the area of the shape , A' the area of the rhombus and A" the area of the four parallelograms
- A"= A - A'
- A" = A -[tex]\frac{d*d'}{2}[/tex]
- A" = 792- [tex]\frac{18*7}{2}[/tex]
- A" = 729 cm²
Let a be the area of the single parallelogram
- a = A"/4 since the parallelograms are congruent
- a = 729/4
- a = 182.25 cm²
the area of a parallelogram is fiven by the formula :
- A = b*h
- b is the base (here y/2) and h the height (here 18/9)
let's find y
- a = [tex]\frac{y}{2}[/tex] * 9
- 182.25*2 = y*9
- 364.5 = y*9
- y = 364.5/9
- y = 40.5
