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3 years ago

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

Mathematics

1 answer:

RUDIKE [14]3 years ago

4 0

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]

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