The image below represents a 12 x 16 room with an 8 x 10 piece of linoleum centered in the room. The yellow and blue rectangles extend the length of their respective sides. Where these two rectangles overlap, there is a green rectangle. In the paragraph box below, explain why the total colored area is 62 square feet.

Since the rectangles are colored in, we can take the area of each color, then add them together. To find all the lengths and widths, subtract as needed: Since the center rectangle's length is 10 feet, subtract 10 from the length of the room which is 16 feet. Those 6 units must be divided in half to give 3 feet for the width of the blue rectangle. Similarly, subtract 8 from 12 and divide the 4 in half to give 2 feet for the width of the yellow rectangle. This also reveals the length and width of the green rectangle. The length is 3 and the width 2, so the area is found 3x2=6. The area of the blue rectangle is found 3x10=30. The area of the yellow rectangle is found 13x2=26. Add these areas up: 6+30+26 = 62 square feet.

eudora eudora · Answer 2 · 2021-10-14T17:22:34+02:00

Area of a rectangular area is given by the expression,

Area = Length × Width

Area of the colored area will be 62 square feet.

Length of bigger rectangle (AB) = 16 feet

Length of smaller rectangle (EF) = 10 feet

Width of bigger rectangle (BC) = 12feet

Width of smaller rectangle (FG) = 10 feet

Since, Length of AB = (x + x + 10) feet

Therefore, (2x + 10) = 16

2x = 6

x = 3 feet

And length of BC = (y + y + 8) = 12 feet

2y + 8 = 12

2y = 4

y = 2 feet

Now area of rectangle ABJI = AB × BJ

= (2x + 10)(y)

= [2(3) + 10](2)

= (16)(2)

= 32 square feet

Area of rectangle IEKD = IE × EK

= x(8 + y)

= 3(8 + 2)

= 30 square feet

Area of colored area = Area of rectangle ABJI + Area of rectangle IEKD

= 32 + 30

= 62 square feet

Therefore, area of the colored area will be 62 square feet.

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