The figure below shows a shaded region and a nonshaded region. Angles in the figure that appear to be right angles are right angles.

A picture of a rectangle is shown. The bottom of the rectangle is labeled 16 ft. The right side of the rectangle is labeled 8 ft. At the bottom left side of the rectangle there is a label that reads 2 ft. Inside the rectangle is a shaded region. The bottom of the region is labeled 8 ft and this side is perpendicular to the left side of the rectangle. The right side of the shaded region has a perpendicular line segment extending upward that is labeled 2 ft. At the top of this line segment is another line segment perpendicular to the right that reads 2 ft. At the end of this line segment is a perpendicular line segment extending upward that reads 1 ft. There is a line segment joining the end of this line segment with the top left corner of the rectangle.
What is the area, in square feet, of the shaded region?
Enter your answer in the box. square feet

What is the area, in square feet, of the nonshaded region?
Enter your answer in the box. square fee

Question

07-04-2015
Mathematics

Answered

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The figure below shows a shaded region and a nonshaded region. Angles in the figure that appear to be right angles are right angles.

A picture of a rectangle is shown. The bottom of the rectangle is labeled 16 ft. The right side of the rectangle is labeled 8 ft. At the bottom left side of the rectangle there is a label that reads 2 ft. Inside the rectangle is a shaded region. The bottom of the region is labeled 8 ft and this side is perpendicular to the left side of the rectangle. The right side of the shaded region has a perpendicular line segment extending upward that is labeled 2 ft. At the top of this line segment is another line segment perpendicular to the right that reads 2 ft. At the end of this line segment is a perpendicular line segment extending upward that reads 1 ft. There is a line segment joining the end of this line segment with the top left corner of the rectangle.
What is the area, in square feet, of the shaded region?
Enter your answer in the box. square feet

What is the area, in square feet, of the nonshaded region?
Enter your answer in the box. square fee

Sagot :

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Hippalectryon Hippalectryon · Answer 1 · 2015-04-07T10:50:40-04:00

Hippalectryon Hippalectryon

07-04-2015

[see picture attached]
Area of part 1:
A1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2
Area of part 2:
A2=length*width=(8+2)*1=10 ft2
Area of part 3:
A3=length*width=8*2=16 ft2

Total shaded area : A1+A2+A3=41 ft2
Total area of the reactangle : A=16*8=128 ft2
Total area of the nonshaded region : 128-41=87 ft2

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