Question

The figure below shows the penalty box and the goal box of a soccer field. The penalty box is the largest rectangle

Answer 1

Part (A):

The area of the penalty box.

The dimensions of the penalty box are (15x-1) and (5x-7)

The area of rectangle = length * width

∴ The area of the penalty box = (15x-1) * (5x-7) = 75 x² - 110 x + 7

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Part (B):

The area of the goal box.

The dimensions of the goal box are (7x-1) and (x+3)

The area of rectangle = length * width

∴ The area of the goal box = (7x-1) * (x+3) = 7x² + 20x - 3

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Part (C):

The area of the penalty box not coverd by the goal box =

The area of the penalty box - The area of the goal box =

(75 x² - 110 x + 7) - (7x² + 20x - 3) = 68 x² - 130 x + 10