Moroccan MosaicThe mosaic above was created in the fourteenth century for a wall in Morocco. Write an expression for each of the following parts of it shown in the detail below in terms of a or b or both a and b. Find:1. The perimeter of the square. 2. Its area. 3. The perimeter of the other rectangle. 4. Its area. 5. The perimeter of one of the trapezoids. 6. Its area. Answers:1. 4a.
The perimeter is just the sum of all the sides. 2. a^2. The area is length times height. 3. 4a + 4b. Add all the sides of the shaded rectangle = a + b + a + b + a + b+ a + b = 4a + 4b. 4. a^2 + 2ab. The length of the shaded rectangle = b + a + b = a + 2b. The height of the shaded rectangle = a. So, the area = a x (a + 2b) = a^2 + 2ab. 5. 4a + 2b Traversing the trapezoid we get, a + a + a + b + a + b = 4a + 2b 6. ab+ b^2 Area of a trapezoid = (width 1 + width 2)/2 x height. width 1 = a width 2 = b + a + b = a + 2b height = b. So, area = (a + a + 2b)/2 x b = (2a + 2b)/2 x b = (a + b)b = ab+ b^2
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