Rectangle, 16cm by 6cm, is inside Semicircle... Find shaded area.

[arkvee]

A rectangle is inside a semicircle. The rectangle has dimensions of 16cm by 6cm. The top two points of the rectangle touch the circumference of the semicircle. And, the bottom two points of the rectangle touch the diameter of the semicircle. The area outside the rectangle but in the semicircle is shaded. Work out the shaded area in terms of pi.

So far I have:
1) Area of rectangle = 16 x 6 = 96 cm²

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2) I do not know how to get the radius of the semicircle to work out the area of the semicircle

 

[Deleted member 4993]

A rectangle is inside a semicircle. The rectangle has dimensions of 16cm by 6cm. The top two points of the rectangle touch the circumference of the semicircle. And, the bottom two points of the rectangle touch the diameter of the semicircle. The area outside the rectangle but in the semicircle is shaded. Work out the shaded area in terms of pi.

So far I have:
1) Area of rectangle = 16 x 6 = 96 cm²

---

2) I do not know how to get the radius of the semicircle to work out the area of the semicircle

You need to show us a sketch!

I cannot see how can two points on a line touch a semi-circle?

 

[arkvee]

 

[lev888]

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2) I do not know how to get the radius of the semicircle to work out the area of the semicircle

Draw some additional lines, you might see something useful.

 

[arkvee]

You need to show us a sketch!

I cannot see how can two points on a line touch a semi-circle?

 

[arkvee]

 

[Steven G]

Draw a straight line from center of circle to
one of the upper corners of the rectangle;
what is the size of the resulting triangle?

You beat me to the bunch line.