Find the area of the shaded portion of the figure. Each vertex of square ABCD is at the center of a circle. Round your answer to the nearest hundredth.

Given:

Each circle has a diameter of 2 inches each.

The outer square has a side length of 4 inches and the square ABCD has a side length of 2 inches.

To find:

The area of the shaded region.

Solution:

Each circle has a diameter of 2 inches. The square ABCD is at the center of each circle so it has a side length of 1 inch.

To determine the area of the shaded region, we subtract the area of the quarter-circles in the square ABCD from the area of the square ABCD.

The area of a quarter-circle

All the quarter-circles have a radius of 1 inch.

The area of 1 quarter-circle

The area of 4 quarter-circles

So the area of the quarter-circles in the square ABCD is 3.1514 square inches.

The area of a square

The area of square ABCD

The area of the shaded region

The area of the shaded region is 0.8585 square inches.

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.

step-by-step explanation: