Question

please explain how to find the blue area​

Answer 1

Answer:

85 units

The short answer is 85 units, and before reading on, you should see if you can get that answer.

One needs to find the lengths of the two shorter sides ('a' and 'b'), perhaps using proportional triangles. If found, then one can determine the inner square area is (a-b)*(a-b). To find a and b, assume I is the point at the upper right corner of the inner square. AIF can be found by Pythagorean rule = root of 1*1 + (.

The side length of the blue square is x inches. The width of the green band that surrounds the blue square is 6 in.

Answer 2

the area of the blue-shaded region is 4 + 3π  or 13.428 cm sq.

Given:

measure of side of the large square = 4 cm

radius of the circles and sectors present in the diagram = 1 cm

To find:

area of the blue-shaded region

Solution:

we can find the area of the blue-shaded region by taking the following steps:

• firstly we have to calculate the area of the large square.

area of the large square = 4 * 4

= 16 cm sq.

• we can simply calculate the area of the blue-shaded region by subtracting the area of the white region from the area of the large square.

• we can note that there are two types of identical shapes that have equal areas. we have to group the identical shapes together which are having the white region.
• let us divide similar shapes into 2 groups namely A And B (Please refer to the image attached here for a better understanding)
• We can see that there are eight shapes for group A and eight shapes for group B.

area of 8 shapes of group A = 8 * area of shape A

= 8 * 1/4 * π r²

= 8 * 1/4 * 22/7 * 1 * 1

=2 *22/7

= 2π

area of 4 shapes of group B = area of small square - the area of circle enclosed in it ( refer to diagram)

= 2*2 - π r²

=4 - π * 1²

= 4 - π

Area of 8 shapes of group B = 2 * ( area of 4 shapes of group B)

= 2* (4 - π )

= 8 - 2π

Area of the blue region = area of the large square - 8 shapes of group A  - Area of 8 shapes of group B

= 16 cm sq. - (4 - π) - (8 - 2π)

= 16 - 4 - 8 +π +2π

= 4 + 3π = 13.428 cm sq.

therefore, the area of the blue-shaded region is 4 + 3π  or 13.428 cm sq.

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