Question

If AB = 9 units, QS = 6 units, and AR = QR = RS, what is the area of the heart shape?

Answer 1

Answer:

Step-by-step explanation:

AR = QR = RS  = (1/2) QS  = 3

 

So ....by the Pythagorean Theorem, AS = AQ  =

 

√ [3^2  + 3^2]   =  √[9 + 9 ]  = √18  

 

And the area of the two  semi-circles= the area of a circle with a radius of AS/2 =  

pi [AS/2]^2 =

pi [√18/2]^2  =  18pi/4  =  (9/2)pi  units^2

 

And the area of the rest of the figure is just that of a rhombus  =

 

The product of the diagonals / 2   =

 

AB*QS/2  = 9 * 6 / 2  = 27 units^2

 

So....the total area  =

 

[(9/2) pi + 27]   units^2   =  about  =  41.1 units^2  [rounded]