Question

The figure contains of two quarter circles and a square what is the perimeter of this figure

Answer 1

Answer: 114.24 in

Step-by-step explanation:

To solve this problem you must apply the following proccedure:

1. You can see two quarter circles. You know that the radius of the circle is 16 inches. Then, the lenght a each quarter of  of the circumference is:

$\frac{C}{4}=\frac{(3.14*16in*2)}{2}=25.12in$

 3. Therefore, the perimeter is:

$P=25.12in+16in+16in+16in+16in\\P=114.24in$

The answer is the second option.

Answer 2

Answer:

Option (2) Perimeter of the figure is 114.24 In.

Step-by-step explanation:

To find the perimeter of the figure, we will find out the perimeters of 2 quarter circles and a square. Then we will add these perimeters to calculate the perimeter of the complete figure.

Now, from the question, the given measurement for a side of the square is 16 in. Since the side of the square is equal to the radius of each quarter circle therefore radius will be 16 in.

Perimeter of the square = 4×(side of the square)

                                        = 4×16

                                        = 64 in.

Perimeter of a circle =  2πr

Therefore perimeter of a quarter circle = (2πr)÷4

                                                  = $\frac{2\pi r}{4}=\frac{\pi r}{2}$

Now perimeter of two quarter circles $= 2(\frac{\pi r}{2})$

                                                                     = πr = 16π

                                                                     = 16×3.14 =50.24 in.

Therefore total perimeter of the figure = 64+50.24

                                                                =114.24 in.