To find the total area that Phillip will be mowing, we need to calculate the area of the rectangular backyard and then subtract the areas of the square cutout and the pond.
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Area of the rectangular backyard: \[ \text{Area}_{\text{rectangle}} = \text{length} \times \text{width} = 20 , \text{feet} \times 25 , \text{feet} = 500 , \text{square feet} \]
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Area of the square cutout: \[ \text{Area}_{\text{square}} = \text{side}^2 = 10 , \text{feet} \times 10 , \text{feet} = 100 , \text{square feet} \]
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Area of the pond: \[ \text{Area}_{\text{pond}} = \text{side}^2 = 8 , \text{feet} \times 8 , \text{feet} = 64 , \text{square feet} \]
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Total area to be mowed: \[ \text{Total Area} = \text{Area}{\text{rectangle}} - \text{Area}{\text{square}} - \text{Area}_{\text{pond}} \] \[ \text{Total Area} = 500 , \text{square feet} - 100 , \text{square feet} - 64 , \text{square feet} = 500 - 164 = 336 , \text{square feet} \]
So, the total area that Phillip will be mowing is 336 square feet.
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