Question

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 feet

Answer 1

the picture in the attached figure N 1

to better understand the problem see the attached figure N 2

Part a) What is the area, in square feet, of the shaded region?
step 1
find the area 1
area 1=b*h/2
b=(8+2)---> 10 ft
h=8-(2+2+1)----> 3 ft
area 1=10*3/2---> 15 ft²

step 2
find the area 2
area 2=b*h
b=8+2----> 10 ft
h=1 ft
area 2=10*1----> 10 ft²

step 3
find the area 3
area 3=b*h
b=8 ft
h=2 ft
area 3=8*2-----> 16 ft²

the area of the shaded region=area 1+area 2+area 3
the area of the shaded region=15+10+16-----> 41 ft²

the answer part a) is
the area, in square feet, of the shaded region is 41

Part b)What is the area, in square feet, of the non shaded region?
step 1
find the area of the total rectangle
area=b*h
b=16 ft
h=8 ft
area=16*8-----> 128 ft²

step 2
the area of the non shaded region=area total rectangle-area of the shaded region
the area of the non shaded region=128-41-----> 87 ft²

the answer Part b) is
the area, in square feet, of the non shaded region is 87