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.

42

step-by-step explanation:

256/6=42

y=mx+b

step-by-step explanation:

m slope, b y-intercept