to solve the problem of finding the shaded area (assuming the common scenario of a square with side length 4 and two intersecting quarter-circles), follow these steps:
step 1: identify key elements
let’s assume we have a square of side length 4. two quarter-circles are drawn inside the square, each centered at opposite corners (e.g., a and c) with radius equal to the side length of the square (4). the shaded area is the intersection of these two quarter-circles.
step 2: calculate area of the two quarter-circles
each quarter-circle has area:
[ \text{area of one quarter-circle} = \frac{1}{4} \pi r^2 = \frac{1}{4} \pi (4)^2 = 4\pi ]
total area of two quarter-circles:
[ 2 \times 4\pi = 8\pi ]
step 3: subtract the area of the square
the union of the two quarter-circles exactly covers the square. the intersection area (shaded region) is the sum of the two quarter-circles minus the area of the square:
[ \text{shaded area} = 8\pi - \text{area of square} ]
area of the square: (4 \times 4 = 16)
final result
[ \text{shaded area} = 8\pi - 16 ]
answer: (\boxed{8\pi - 16})
作者声明:本文包含人工智能生成内容。
