The diagram shows a square with perimeter 20cm.

The area of the shaded region is 16.2 cm square and this can be determined by finding the area of the non-shaded region and subtracting that area by the area of the square.

Given :

Square with perimeter 20cm.

The perimeter of a square is given by:

20 = 4a

a = 5 cm

Now, to find the area of the shaded region, first find the area of the non-shaded region and then subtract that area by the area of the square.

The area of the non-shaded area is given by:

Total Area =

The total non-shaded area = 5 + 3.5 = 8.8 cm square

The total area of the square = 5 5 = 25 cm square

Now, the area of the shaded region is given by:

A = 25 - 8.8

A = 16.2 cm square

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Explanation:

Let

A = area of entire square

B = area of white triangle in the bottom left corner

C = area of white triangle in the upper right corner

D = area of the gray shaded quadrilateral

The perimeter is 20 cm, so each side is 20/4 = 5 cm. The area of the square is therefore A = 5*5 = 25 square cm

The white triangle in the lower left corner has a base of 5 cm, and a height of 5-3 = 2 cm, so

B = 0.5*base*height = 0.5*5*2 = 5

The white triangle in the upper right corner has a base of 5-3.5 = 1.5 cm and a height of 5 cm, so its area is

C = 0.5*base*height = 0.5*1.5*5 = 3.75

In summary so far we found that:

A = 25

B = 5

C = 3.75

This means the gray shaded area is

D = A - B - C

D = 25 - 5 - 3.75

D = 16.25

We start with the overall area (25), then kick out the white areas where they aren't shaded (5 and 3.75). This leaves the gray shaded area to be 16.25 square cm. Divide this over the original square area to get

D/A = (16.25)/(25) = 0.65 = 65%

the answer is b i just did that

step-by-step explanation:

i found two solutions,   n = 2 • ± √3 = ± 3.4641

step-by-step explanation: