Question

Find the area please :)

Answer 1

Have a look at the attached image. Figure 1 is the original diagram. Figure 2 is where I introduced an extra line to cut the L shape into two rectangles. I'll be using figure 2. I've also denoted the rectangles as rectangle A in blue, and rectangle B in red. 

Let's find the area of each individual rectangle

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Area of Rectangle A = (length)*(width)
Area of Rectangle A = (2x+2)*(3x+1)
Area of Rectangle A = 2x*(3x+1)+2*(3x+1)
Area of Rectangle A = 2x*3x+2x*1+2*3x+2*1
Area of Rectangle A = 6x^2 + 2x + 6x + 2
Area of Rectangle A = 6x^2 + 8x + 2

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Area of Rectangle B = (length)*(width)
Area of Rectangle B = (10x+8)*(4x+3)
Area of Rectangle B = 10x*(4x+3)+8*(4x+3)
Area of Rectangle B = 10x*4x+10x*3+8*4x+8*3
Area of Rectangle B = 40x^2 + 30x + 32x + 24
Area of Rectangle B = 40x^2 + 62x + 24

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The total area is equal to the sum of the individual rectangle areas

Total area = (area of rectangle A) + (area of rectangle B)
Total area = (6x^2 + 8x + 2) + (40x^2 + 62x + 24)
Total area = 6x^2 + 8x + 2 + 40x^2 + 62x + 24
Total area = (6x^2+40x^2) + (8x+62x) + (2+24)
Total area = 46x^2 + 70x + 26

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The final answer is therefore 46x^2 + 70x + 26