In the figure above, semicircles X and Y have radii of 6 and 8 feet, respectively, then what is the area of semicrcle Z (in square feet)? (Note: figure not drawn to scale)
A. 10Ï€
B. 20Ï€
C. 25Ï€
D. 50Ï€
E. 100Ï€
The OA is D.
With the radii of semicircles X and Y I can get the diameter of semicirlce Z (using Pythagoras Theorem) and then I can get it area, right?
I appreciate if any expert explain it for me this PS question. Thank you so much.
Hi AAPL,
Let's take a look at your question.
Radius of the semi circle X = 6 ft
Diameter of the semi circle X = 12ft
Radius of the semi circle Y = 8 ft
Diameter of the semi circle Y = 16 ft
We can find the diameter of the semi circle Z using Pythagoras Theorem,
$$Diameter=\sqrt{12^2+16^2}$$
$$Diameter=\sqrt{144+256}$$
$$Diameter=\sqrt{400}=20$$
Radius of the semi circle Z = 20/2 = 10
$$\text{Area of Semi Circle Z}\ =\ \frac{1}{2}\pi r^2$$
$$\text{Area of Semi Circle Z}\ =\ \frac{1}{2}\pi (10)^2$$
$$\text{Area of Semi Circle Z}\ =\ \frac{1}{2}\pi (100)$$
$$\text{Area of Semi Circle Z}\ =\ 50\pi$$
Therefore, Option
D is correct.
Hope it helps.
I am available if you'd like any follow up.
