Question

HURRY HELP PLEASE!!!

Type the correct answer in the box.  Assume that π = 3.14, and round your answer to the nearest hundredth.



The figure shown is formed by the arcs joining the midpoints of the four sides of a square with a side length of 15 centimeters.

The area of the shape is __________ square centimeters.

Answer 1

48.38

Step-by-step explanation:

I took the test on Edmentum/ PLATO and it was correct.

Answer 2

Answer: The area of the shape is 48.38 square centimeters.

Step-to-step explanation:-

The side-length of square = 15 cm

Area of square =
`(\text{side}^2)=15^2=225\ cm^2`

Since, the figure shown is formed by the arcs joining the midpoints of the four sides of a square, the radius of the quadrant =
`(15)/(2)=7.5\ cm`

Since, all the interior angles in a square is a right angle, therefore, each quadrant is a sector of 90° in a circle of 7.5 cm radius.

Area of each quadrant=
`(90^(\circ))/(360^(\circ))\pi r^2`

=
`=(1)/(4)(3.14)(7.5)^2=44.15625\ cm^2`

Now, Area of shaded region = Area of square -4 × Area of quadrant

=
`225-4*44.15625=48.375\approx48.38\ cm^2`

Hence, The area of the shape is 48.38 square centimeters.