✔ 最佳答案
1.
Using the formula of area of sector and area of triangle, we can find that area of one of the inner shaded region = 2 x (area of a quadrant - area of triangle) = 2 x [p(1/2)^2/4 - (1/2)(1/2)(1/2)] = 2 x (p/16 - 1/8) = p/8 - 1/4 where p = pi.
So area of 4 inner shaded area = 4(p/8 - 1/4) = p/2 - 1.
From the diagram, we can get
Area of big circle - area of 4 small circle = 4 times the outer shaded region - 4 times the inner shaded region (because the inner regions have overlapped). That is :
p(1)^2 - 4p(1/2)^2 = p - p = 0, that means area of 4 outer shaded region = area of 4 inner shaded region = p/2 - 1.
So total shaded area = 2(p/2 - 1) = p - 2.
Q2.
Let length of side of bigger square = x.
Area of triangle ADE = x(x - 4)/2.
Area of triangle ABC = x(x + 4)/2.
Area of triangle EFG = (4)(4)/2 = 8.
Sum of area of 2 squares = x^2 + 16.
So area of triangle AEG = x^2 + 16 - [x(x- 4)/2] - [x(x+4)/2] - 8
= x^2 + 16 - x^2/2 + 2x - x^2/2 - 2x - 8
= 8.
