Question

Phillip is mowing his backyard. His backyard is oddly shaped.

The rectangular backyard with length 20 feet and width 25 feet has a square of side length 10 feet cut out from its right bottom corner.

Phillip has an 8 ft by 8 ft pond in his backyard. What is the total area that Phillip will be mowing?
Responses

64 square feet

64 square feet

106 square feet

106 square feet

336 square feet

336 square feet

400 square feet

Answer 1

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.

1. **Area of the rectangular backyard**:
\[
\text{Area}_{\text{rectangle}} = \text{length} \times \text{width} = 20 \, \text{feet} \times 25 \, \text{feet} = 500 \, \text{square feet}
\]

2. **Area of the square cutout**:
\[
\text{Area}_{\text{square}} = \text{side}^2 = 10 \, \text{feet} \times 10 \, \text{feet} = 100 \, \text{square feet}
\]

3. **Area of the pond**:
\[
\text{Area}_{\text{pond}} = \text{side}^2 = 8 \, \text{feet} \times 8 \, \text{feet} = 64 \, \text{square feet}
\]

4. **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**.