Question

In: Physics

Determine what fraction of the figure is shaded. (a) A four unit wide by four unit...

Determine what fraction of the figure is shaded.

(a)

A four unit wide by four unit tall Geoboard is made up of 25 points. A shape consisting of five connected line segments and a shaded region is on the Geoboard.

The first segment starts one unit to the right of and one unit above the bottom left corner of the Geoboard. It goes right two units.

The second line segment starts where the first line segment ended. It goes up and right and ends two units above the bottom right corner of the Geoboard.

The third line segment starts where the second line segment ended. It goes up and left and ends two units to the right of the top left corner of the Geoboard.

The fourth line segment starts where the third line segment ended. It goes down and left and ends two units above the top left corner of the Geoboard.

The fifth line segment starts where the fourth line segment ended. It goes down and right and ends where the first segment started.

The region is trapezoidal and fills the bottom portion of the shape from left to right. It is one unit tall, two units wide at the base, and four units wide at the top.

(b)

A four unit wide by four unit tall Geoboard is made up of 25 points. A shape consisting of five connected line segments and a shaded region is on the Geoboard.

The first segment starts at the bottom left corner of the Geoboard. It goes right four units.

The second line segment starts where the first line segment ended. It goes up two units.

The third line segment starts where the second line segment ended. It goes up and left and ends one unit to the left of the top right corner of the Geoboard.

The fourth line segment starts where the third line segment ended. It goes down and left and ends two units above the bottom left corner of the Geoboard.

The fifth line segment starts where the fourth line segment ended. It goes down and ends where the first segment started.

The region is rectangular and fills the bottom portion of the shape from left to right. It is one unit tall, and four units wide.

(c)

Expert Solution

It is not mentioned whether the fraction of the region to the geoboard or to the figure is to be found out. Both has been done

a)

The geoboard and the corresponding lines are shown in the image below

The region is shaded with green color in the figure below.

The area of region 1 and 4 will together give 1 square units. 2 and 3 will contribute 1 square unit each.

Total area of shaded portion = 4 squts

Total area of the geoboard = 16 squts

Fraction of shaded region to the geoboard = 4/16 = 1/4.

Area of image = 7 squts

Fraction of shaded region to the image in the geoboard = 4/7

b)

The geoboard and the corresponding lines are shown in the image below

The region is shaded with green color in the figure below.

Total area of shaded portion = 4 squts

Total area of the geoboard = 16 squts

Fraction of shaded region to the geoboard = 4/16 = 1/4.

Area of image = 12 squts

Fraction of shaded region to the figure in the geoboard= 4/12 = 1/3

genius_generous answered 2 years ago

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