2) find the area of the shape. a) 39 square yards b) 56 square yards c) 72 square yards d) 108 square yards

72 square yards

There are numerous ways to decompose the area into parts for which you have a formula: rectangle, square, trapezoid.

An obvious one is the separately figure the area of the 3×6 tab at the right and the area of the 9×6 rectangle to its left. Then the area is ...

... 54 yd² +18 yd² = 72 yd²

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You can cut off the tab (EHCD in the attachment) and add it to the top to make a 12×6 rectangle with an area of 72 yd².

Or you can cut half the bottom "tab" off (AIJF in the attachment) and fill in below the tab to the right, making a 6×12 rectangle with an area of 72 yd².

The whole top part (GBCD in the figure) can be considered as a 3×12 rectangle with an area of 36 yd². That area will be added to the 6×6 square below which also has an area of 36 yd². Those two figures total 72 yd² in area.

You can treat the figure as having a 6×6 square cut out from the bottom right corner of a 9×12 rectangle. Then the area is figured as 108 yd² - 36 yd² = 72 yd².

Drawing a line (BE in the attachment) between upper left outside corner and the inside corner divides the figure into two trapezoids. The bottom one has bases 9 and 6 and height 6; the other has bases 6 and 12 and height 3. The areas of those figures are 45 yd² and 27 yd², for a total of 72 yd².

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

your answer is d 2,500

step-by-step explanation: