## wafflegod551 3 years ago A sign designer created a sign in the shape shown below. The semicircles are congruent to one another with a diameter of 8 inches. What is the perimeter of the sign? about 120 inches about 135 inches about 108 inches about 75 inches

1. wafflegod551

2. pfenn1

I would calculate the area of the rectangle (without the semicircles cut out) and then subtract the areas of the semicircles from that. So the area of the rectangle would the height (h=30 inches as given) and we know the width(w) is the width of 3 half circles with diameters of 8 inches so w = ? Can you figure that part?

3. mubzz

The perimeter is the sum of all the boundary dimensions of any figure. The boundary of this figure has two sides and 6 semi-circular arches. The perimeter will be computed by: Perimeter = 2*(Length of side) + 6*(arc length of single semicircle) \[Perimeter = (2*30) + 6(pi*radius)\] where radius is diameter/2 = 4 inches Perimeter = 60 + 6(\[4pi\] Perimeter = 60 + 24pi Perimeter = 135.408inches

4. pfenn1

Now, what is the area of the 6 half-circles that have been cut out of the rectangle? 6 half-circles make 3 whole circles and we know the area of a circle is (pi)(D/2)^2 where D is the diameter so....

5. wafflegod551

ty :D

6. pfenn1

Shoot...I was figuring out the area, not the circumference . Ooops.

7. wafflegod551

well at least you tried lol