Question

The diagram shows a square with perimeter 20cm.

Answer 1

Answer:  65%

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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

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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

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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%

Answer 2

Each side of the square has length 5cm.

Area of shaded part = Area of square - Areas of triangles.

25cm2 - 0.5 * 1.5cm * 5cm - 0.5 * 2cm * 5cm = 25cm2 - 3.75cm2 - 5cm2 = 16.25cm2.